So, we are continuing our look at binary circuit codes. So, we look for this ring Rm, this is the cyber polynomial, primary polynomial, primary degree is less than or equal to, degree is less than or equal to n minus 1. And addition and multiplication are done to expand to a complex. I mean I do not really have to say addition is done modulo expand plus 1. So, the multiplication really it makes a difference. And then we saw cyclic codes are basically ideals from Nare. And then we saw the definition of an ideal, we saw that multiplication by x is the same as the synthesis, because of which ideals become cyclic codes. And then we saw the generator polynomial. So, we saw all ideals are useful in Rm. So, that an ideal i, cyclic code will be thought out of the integrated by g of x. Not only that, different polynomials and so only this we can have a special g of x, a pressure generator, which is the least degree, least degree polynomial in i. So, I can say there least degree polynomial on i, because if there is only one, if you do not have multiple least degree polynomials, it is unique. And not only that, we know that Vfx divides x bar n plus 1. So, there is lots of nice properties that ideals in Rm satisfy. And that is good. And then the last result that I showed for you is, if you have an ideal, we will generate the over facts. If I tell you who had over facts divides x bar n plus 1, this implies what? Fx is the generator polynomial of i. So, over facts is the generator polynomial of i. The reason is, if you had a lower degree polynomial in i than fx, that also has to divide x bar n plus 1. And fx also divides x bar n plus 1. So, in all these things together, you can put it together maybe. You do not even need that, that provides a better result. So, let us see. I think it has to work out in some nice way like that. So, I think let me write down a proof. I think I have done a proof. I will see what is needed. So, suppose Vfx equals mfx times over facts in Rm. So, what do you mean by saying gfx is mfx times afx in Rm? Actually, gfx is over facts times over facts in f2x. And then what should I do? I should do modulo x bar n plus 1. So, that is how it works. So, when you have something like this, what is true is gfx has to be equal to mfx times afx plus some bfx times what? x to the power n plus 1. So, we know that fx also divides x bar n plus 1. So, you will have afx times mfx times bfx plus some efx. So, what is this efx? So, we know if you see this. So, this is true. We know. So, this is a nicer way of writing it down. x bar n plus 1 is some afx times efx. All this is in f2 only. Without any modulo. So, this will have to be true. Now, gfx is here which means clearly what? You cannot have the degree of gfx being lesser than the degree of afx. So, this is in what? In f2x. Is it fine? No? Yes, maybe. So, afx has to divide gfx in f2x itself. So, that clearly implies it will have to work. So, if you have afx times efx, what will be the degree of efx? Oh my God. Degree of efx will be n minus the degree of afx. So, that has to work. So, efx has degree n minus that and you can also look at the degree very carefully if you like. But this has to work out. This is in f2x itself. Which means afx has to divide gfx in f2x. So, this is basically a rewriting of the proof that I said that if you have a generator polynomial, then it has to divide x parent plus 1 and then every other element of the ideal has to be a multiple of the generator polynomial in f2x. So, pretty much the same proof you can redo like this and we will get the answer. So, the same idea is used here. So, this has to work out. So, you cannot have gfx being lesser degree than afx. So, same this afx is okay. So, at least that not just a little bit. So, this prototype of the generator polynomial has, gives us immediately one nice characterization of the circuit code. If you have an ideal being generated by gfx and gfx is the generator polynomial. And let's say the degree of gfx equals g0 plus g1x plus grx to the power r. The first thing is when I say degree of gfx is r, gr will not be 0. If it is 0 then the degree will be not r. I can also argue that g0 will not be 0 in the generator polynomial. How do you argue that? Yeah, you can take an x out of the remaining and then what will happen? What is inside? But how do you know that that's in the ideal? It's a time step, no? Yeah. So, it's a cyclic shape stuff. What is inside? So, obviously if you do enough cyclic shapes, you will go back to what's inside. So, this is 0 when we can produce some other element in the ideal which has lesser degree than r. So, this will also not be 0. So, these two things you can keep in mind. So, gfx is degree r. I can now find the size of the ideal. Okay? Where is that? If I were to know, I don't know is the set of all multiples of nfx times gfx. Okay? So, it's not right. Degree of nfx? What can I say about degree of nfx? Let's go n equal to n minus r minus 1. Where can I say that? As you know, every multiple of gfx in f2x of degree less than or equal to n minus 1 is in the ideal. Okay? So, both ways it works, right? If any multiple of gfx is definitely in the ideal, there's no problem. But I know all elements of i can also be or also multiples of gfx in f2x. So, if you only do multiplication in f2x, when will I get polynomials inside rm? Only when the total degree is less than or equal to n minus 1. So, if gfx is simple as degree r, you cannot make nfx of degree greater than n minus r minus 1. So, degree has to be less than or equal to n minus r minus 1. Only then the product where I have degree, product where I have degree less than or equal to n minus 1. And I'll have all the elements of i. Okay? I don't have any other elements. So, from here, size of i can be equitifunded. Size of i equals what? 2 power m minus 1. Okay? So, that's the number of nfx that I can have. Okay? So, that's the degree less than or equal to n minus r minus 1. It means n minus r coefficients are there in mfx. So, you pick either of them, 1 or 2, 1 or 2 is 2 power m minus 1. Okay? So, gfx gives you that. Not only that, if you know that i use a cyclic code, right? This idea also gives you the generator matrix. Okay? You can find the generator matrix. So, this clear basis vector solve this case. The very easy generator matrix is to put gfx in the first row. What do I mean when I say gfx in the first row? You put g0, g1, all the way through. The r, and then you fill the remaining with r. Okay? So, remember, the third one, that's the end, right? Okay? And then I can now shift. I can do x times gfx in the second row. Okay? And what will be x times gfx? Let's 0 here, d0, 0, not 0. gr minus 1, gr, 0 all the way. Okay? And then how many shapes do you have to do? The last one will be x bar 1 minus r minus 1 times gfx. Okay? But we'll put gr over the very end point. So, we'll have some g0 to gr. Okay? And that will be the generator. Where will that be the generator? You can see that in this multiplication.   Okay? So, if we view each of these gates as a vector, I get this generator. Okay? So, every codeword, remember this is a codeword. You can pick up it as a codeword polynomial, which will be c0, c1 all the way to cn minus 1. In terms of polynomials, it will be c0 plus c1x plus around full cn minus 1, x power n minus 1. Okay? So, this polynomial is equal to the sum of all these gates. And if you vary m0 to mn minus r minus 1, I get different codewords. So, that means clearly this is the basis, not too hard to argue that this is the generator polynomial. All these things, I think we saw briefly, but anyway. So, it's good to go over these things once again. So, this is the main idea. The main idea is the way this proof goes. Any element of this ideal, if I say it's generated by a divisor of x power n plus 1. It's important that it should be a, it should be something that divides x power n plus 1. Yeah, we have used that very clearly here. Then it will turn out that any element should be a multiple of gfx in f2, f6. And that gives you all the required properties. Okay? So, that's about these guys. So, now you're going to go on and try and list out all the possible cyclic codes. So, of course, if I have to go back to the first property here, the important property is this thing. Okay? If I list out all the divisors of x power n plus 1, I have also listed out all the cyclic codes of length n. Right? I don't have to really worry about that. Okay? So, all divisors of x power n plus 1. Of course, the divisor should have binary precision. That's part of the restriction. gfx has binary coefficients. So, now the point is, how do I do this? How do I assign divisors of x power n plus 1? You already know the answer. Okay? So, let me do that a little bit more slowly. So, let's say, part 3 of x power n plus 1. Okay? So, the first thing is, we will pick n to be odd. Okay? If n is 0, and if n is 0, x power n plus 1 will have repeated rules and all kinds of confusion will happen. So, if n is even what will happen? So, what do I do if n is even? Say, n is 2 times m. And I can write this as x power n plus 1 whole square. So, I can keep on removing factors of 2 till I get an odd number. Okay? So, it will be some x power odd number plus 1. We'll raise to the part some power of 2. Okay? I can go down to that level. So, I can remove all 2's from n. Okay? So, I'll assume n is odd and only factor that. Okay? So, usually, whenever we think of cyclic codes, binary cyclic codes, n will always be odd. Okay? You won't have an even length cyclic code. I'll tell you more about these things later on. Okay? So, now you have n being odd. So, if you want to factor x power n plus 1, you know it's the same as finding n troops of unity. Okay? So, if you want to find some number which then raise to the power n will give you 1. Okay? So, it's the same as finding some element in a large enough feed which has ordered equal to n. Okay? So, it's good to find elements like that. Okay? So, you can show a lot of things about x power n plus 1. In fact, when n is odd, x power n plus 1 and it's derivative, whether it's derivative, formal derivative, n next to the power n minus 1. So, n is odd, it's going to be the x power n minus 1. And x power n minus 1 and x power n plus 1 don't have any common factors. They're relatively prime. Okay? So, it can never have repeated roots if you have n being odd. Okay? So, that's the standard result in polynomial stuff. Okay? So, if you want the polynomial to have repeated roots, polynomial and its formal derivative, okay, should have some GCD which is not one. They should have some common factor. Okay? The repeated root will occur both in the polynomial as well as in its derivative. Right?  Two times x plus 1. So, derivative also has that as a root. You can show this. It's not very hard to show. Okay? So, clearly it won't have any repeated roots and there are various other ways of showing it. At this point, I can prove it to you in various ways. Initially, if you want to develop it, that's how we do it. Okay? So, n is odd. You need to find some, let's say, alpha, which is 3 up to power n. That's what. Other than alpha equals alpha. Okay? If n is odd, it turns out this is always possible. Okay? So, if n is odd, there exists m in first step. So, n odd, there exists n in first step. n divides 2 power n minus 1. So, this is the fact which you can prove using various results. I think we proved it earlier in class also. I'm not going to repeat it. Okay? But this is true. Okay? There exists n. First step, n divides 2 power n minus 1. In fact, usually you pick the smallest n. Smallest n is usually chosen. Okay? Once you have this, okay, what you do is, if you have beta and gf 2 power n in perimeter, you can set alpha to be equal to what? Beta power 2 power n minus 1 over n. Okay? This is what we're going to set it to be. Okay? So, that's what's for all these things. It's a little bit confusing. Okay? So, if you do this, then order of alpha is going to be equal to n. Okay? So, I know x bar n plus 1 has no repeated roots. And if you have an element of order alpha, order n and gf 2 power n, so I can find n roots for x bar n plus 1. Okay? So, alpha to the root of x bar n plus 1. In fact, alpha, alpha squared, alpha power 3, so on till alpha power n minus 1. And all these things will set, x bar n plus 1 in gf 2 power n. Okay? So, I've just seen before that, let me repeat that once again. It's rather repeating. Okay? So, if alpha did not have order n, then this cannot be distinct. Okay? I won't be able to argue that. But since it has order n, I know this is distinct. Okay? Once this is true, I know I can easily write x bar n plus 1 over s x plus alpha times x plus alpha squared. So, I'll go over that one. Okay? So, alpha power n minus 1. Is it okay? Did I get it right? No, no, no. I'm sorry. You also have one. Okay? So, you also need one which you can write it as in any which way you want. So, let's write it in the beginning itself. So, x bar n plus 1. Okay? So, one nice thing about this result is, we see that x bar n plus 1 factors into linear factors. That's a nice thing in this. But the only not so nice thing is that you have to deal with no gf2 parameter. Okay? You don't have binary factors. There's only one binary factor. Okay? Right? Everything else is non-dynamic. Okay? So, you have to now call upon your cyclotomic process idea and then combine the terms and get minimal polynomials which will now be binded. Okay? So, that's something we have to do. So, for that, you have to find. So, next, what we have to find cyclotomic process. This guy. Modulo n under multiplication by 2. Okay? So, you will have so many cyclotomic process. Then, according to the cyclotomic process, we group your powers of alpha and put your factors. And when you multiply all the factors inside the cyclotomic process, what will you write magically? You will get a binary polynomial and that will be reducible in binary analysis. Okay? So, that way you can group the linear factors together according to cyclotomic process to get binary factor. Okay? So, this is the general idea that we've been using. But, yeah, so the process themselves give you the degree of the polynomial. Okay? So, depending on the cyclotomic process, depending on the slight size of the cyclotomic process, you know what degree that polynomial will have. If you want to exactly find that polynomial explicitly, you should do some multiplication in gf2 param, which you may not want to do. If you don't want to do that, at least the degree is there. Okay? So, the degree itself gives some information for us. Okay? So, that's what we're going to do. So, I'm going to take a couple of examples. And let's take this. For example, I'll take 1 equals 9. Okay? So, if you do that, the first thing you have to find is in which Galois field you have the primitive ninth root of unity. Okay? So, you may not even need to find it. Okay? So, let's try to find the cyclotomic process. Okay? So, remember, the set I'm working for is 1, 2, 3, 4, 5, 6, 7, 8. That's what I'm working with, the cyclotomic process. I'm going to take the elements and do this partitioning of the cyclotomic process. The first thing we'll do is go. Okay? Next, when I start with 1, I'll have 1, 2, 4, 8, 7, 5. That's it. Okay? That will be the first cyclotomic process. Next, you have to see what is left out. 3, 3, 6, 6. Okay? And that carries everything. Okay? So, I have 3 cyclotomic process. So, I'll call the first one as C0. This one, I'll call C1. This one, I'll call C3. Okay? So, it's usual to pick the smallest element in a cyclotomic process and make it the representative of the process and call it C3. Okay? So, if I do this, it turns out that it will be so, x star n plus 1 will factor into 3-parameters and 0 affects and 1 affects and 3 affects and 0 affects will do what? x plus 1 and 3 affects will do? x star n plus x plus 1. Okay? So, how do I know that it will be x star? How do I know it will be x star plus x plus 1? It's a polynomial of degree 2 Yeah. It's a polynomial of degree 2 and it has a reducible that immediately tells me it has to be x star plus x. Now, everyone affects on multiple possibilities. We can pick the primitive 6-degree polynomial which is possible to pick that. There will be some tables for it but I know that the degree is 6. Okay? It has got degree 2, degree 1. Okay? So now, if I want to enumerate all cyclic curves of length 9, okay? So, I have to just list out all possible generator polynomials. Okay? So, what are the different possible flow effects? Okay? And k also, right? k is basically the dimension. Okay? So, if I want to write down cyclic codes and make this 9, I have to list out the possible gfx. What are the different possible gfx? The first one would be 1. Okay? So, it's always a trivial thing. And that will give you k equals 9, right? So, degree n minus degree so, it will be equal to 9. Okay? And then, next one is x plus 1 by itself. That will give me k 8. In fact, this will be the real name code. 2 by identity code. How do I know it will be the even weight code? Yeah, 1 is the real. Right? So, all code words are multiples of x plus 1. So, what will happen if I put x equal to 1 and c of x? Right? If it is 0. Okay? So, c of 1 is 0 means what? c of x is c0 plus c1x plus c2x plus so on. If I put x equals 1, I basically get the parity. Okay? c0 plus c1. That is 0 means the parity is 0. So, it gives me the even weight code. So, x plus 1 always generates the even weight code. So, it is an easy way to keep in mind. So, what else do you have? x plus 1 plus 1. Right? What will be the dimension here? 7. So, this code is a... It is an interesting way to call it. That is really no useful property. Okay? So, you can think about it as various ways of thinking about it. But, x plus 1 is 7. 9 and 7, it has... It cannot have a minimum distance 3. Can it have a minimum distance 3? A 9 and 7 code? Let me see if you remember. Can it have a minimum distance of 3? How do you answer this question? Don't think in any other way. Okay? A 9 and 7 code has to have a parity check matrix. Right? It will have 9 columns. How many rows will it have? 2. 2 rows, 9 columns. Can you have minimum distance 3? It is impossible. That is how you answer these questions. Okay? Don't think... Good things. When I have this question of minimum distance, it makes the only way to answer it is with the parity check matrix. Okay? So, there should be other methods. But, usually, parity check matrix will come clear. A 9 and 7 will not have a minimum distance. Can it have a minimum distance of 3? Can it have a minimum distance of 3? A 8 and 5 is one of the values. What? What are you saying? Think about it. Rank is not the problem, man. Oh, my God. I forgot to know the definition of minimum distance. What is the definition of minimum distance? All the entries are binary, right? Binary? Obviously, it's binary. These are all binary. I'm talking about binary cyclic codes. If I didn't have binary cyclic codes, why am I worried about combining the factors together? I won't even worry about that. So, binary. 9 and 7 code over a suitably large alphabet can have minimum distance of 3. No problems with that. But, binary cannot have that. Okay? So, when you go to the... You cannot have more than 3 columns. 4th column will tell you. So, extraplegicly, one is not a very interesting code. And then, what else can I do? Okay. It's all right. XQ plus 1, I can go to. What is XQ plus 1? Basically, the product of these two. So, if you don't want to do a multiple question, you can do this. Write it like this. And that will have 6 dimensions. Can you say anything more about that code? XQ plus 1? What do you think that would be? I'm sorry. It'll actually be even weight. It'll be a subcode as an even weight code, right? Okay. Any other comments? Minimum distance, etc.? Minimum distance is 2, right? It's got XQ plus 1. So, yeah. Definitely, minimum distance is 2. So, it's not very interesting from error correcting and all point of view. Minimum distance is going to be 2. How do I find minimum distance 2? It's clear, right? But XQ plus 1 is a problem. And that does not mean weight 2. So, it's clearly minimum distance 2. Okay. And then, what else? What is the next one that is interesting? It's this N1Fx. Okay. I don't know what it is. But I know it is grad degree? 6. So, what will be K? 3. Okay. What can I say? Can I say anything about this code? Can I say anything about the minimum distance of this code? Okay. So, it turns out that it's something called the BCH bound that we saw. We didn't see it in the volume of generality. So, I'll do it later on. But that's the only thing you can use for quickly finding minimum distance. Otherwise, you have to go and say, you find the target matrix and actually find something like that. You'll answer it. You can't answer very precisely. So, it turns out if you use the BCH bound, what is called the BCH bound, which I'll do later on, which basically relates the minimum distance to the number of roots that are consecutive. Okay. So, here you can find that there are two consecutive roots. One, two. Right? Not more than that. So, the minimum distance is definitely greater than or equal to three. Okay. That's the only thing you can say. Okay. Anyway, we'll come back to that later on. So, the dimension is three. That's easy enough to do. What else can we do? Anything else? X plus 1 times M1x. Right? This I can do, no? What would be the k there? Two. Okay? What can I say about this, right? Yeah. So, there are various things you can do, the BCH bound, even rate, et cetera. Lots of these things you can say. So, what else do you have here?  And that would be one. Okay? What code is that one? Appetition. So, how would I find this repetition code? What will I get if I multiply these two things? 1 plus X plus X squared plus so on till X star 8. Okay. So, let's see. What do you think M1 of X will be? Okay. So, this is X star 9 plus 1. What will M1 of X be? Yeah. It's going to be X star 6 plus X star 3 plus 1. Do you get that? Okay. What will M1 of X be? What? Yeah.  Right? So, it will end up being 1 plus X star 3 plus X star 6. So, you can, in fact, find M1 of X also explicitly if you like. So, all these things will also have some reasonable parts.  And it has got dimension 3. Okay? And this is GSX. Okay? So, once you know that 1 plus X star 3 plus X star 6, you can say something more about this code.  Okay. Every star will repeat. Will repeat, right? So, you see, M1 of X is going to be the, no, M1 of X is this bit. So, the message polynomial has degree only less than or equal to 2. Okay? So, if I take a polynomial of degree less than or equal to 2 and multiply with this, in fact, every code word will have to stop. It will be some N0, N1, N2. And then what will happen? The same thing will repeat N0, N1, N2. And then, another N0, N1, N2. So, this is basically the repetition code in this case. Okay? It's basically the same as 3 repetition cells, the 3, 1, 3 code. Okay? So, it's basically the same as the 3, 1, 3 code. Instead of repeating N0, N0, N0, M1, M1, M1, M2, M2, M2, I'm doing some good permutations just for fun and doing M0, M1, M2, M2, M1, M2, M1, M2. So, clearly there is no under the name of the sentence 3. Okay? You can also do it using bc's bound and all that, if you don't know M1 effects. You know M1 effects explicitly like in this scenario, you can find a lot more details about how the code will look. Okay? So, you can look at this there. What will be x plus 1 times M1 effects? Just 1 plus x, 1 plus x, 1 plus x, 1 plus x. Yeah.  So, it's something like this and it has to have even weight. Okay? So, when will it have even weight? You have to think about it. So, you're repeating it 3 times. So, the weight of this, you can find, yeah, should, what do you mean each of them? Should I use them? Yeah. So, out of M0, M1, and M2, 2 of them should have, I mean, yeah, something like that has to happen. So, you can think about it that way and find out some more things. The repetition code anyway is quite easy. Okay? So, that's it. Those are all basically codes of length 9. For instance, there is no cyclic code of dimension 5. There's no cyclic code of dimension 4. Okay? Right? So, actually only 5 is the non-previous statement. From there, I can quickly go to the other thing. How will I do that? If there is no cyclic code of dimension 5, how do I know that there cannot be a cyclic code of dimension 4? Yeah, it's real, right? If there is a cyclic code of, there's no cyclic code of dimension 4, there cannot be a cyclic code of dimension 5 else. If there is a cyclic code of dimension 5, which dual will also be cyclic, that will be a dimension 4 cyclic code. So, you can quickly rule out these cases. So, 5 and 4 are not possible for cyclic codes. Okay? So, it's kind of like a non-trivial result, which you cannot show directly. Okay? So, if you just call some guy at the street, you know he's able to do that, and say can you show that there's no cyclic code of dimension 5 with length 9? It's slightly non-trivial. It's not very clear why it should be infinite. It shouldn't be infinite. Okay? It comes from the factoring of h per 9 plus 5. 9 plus 1, it has only 7 types of factors. The hint and a set of factors, those powers add up to 5. So, that's the idea. So, it's slightly non-trivial. Okay? So, let's do maybe one more example, which is a little bit more interesting. Maybe. Okay? I'll take 1 equals 21. Okay? So, 21 is interesting enough. So, if I do cyclic dynamic process once again, I'll add 0. Then I'll have 1, 2, 4, 8, 16, 11. Okay? And then I'll add 3, 6, 12, that's it. And then I'll add 5, 10, 20, 19, 17, 14. Right? And then I'll add 7, 14, that's it. Okay? And then I have 9, 18, 15, that's it. Okay? So, you will have an M0 of x, which is x plus 1. Then you have an M1 of x of degree, 6. Then you have an M3 of x of degree, 3. Have an M5 of x of degree, 6 again. And then you have an M7 of x, which will actually be x plus x plus 1, okay? It cannot be anything else. Then you have an M9 of x. Okay? That's all the factors that are. Right? So, these are all the, these are all the modifications. So, now if you want to write down all cyclic codes and write down g-effects and then k, right? It's a little bit more messy, you know? I mean, you have so many more codes, but you have to pay some attention to it and then do it. Of course, you have the 1 and the x plus 1 and all that. So, you can get to the part quite easily. Then you will have x plus 1, 20, once again, the even rate code. And then the next one would be, you know, 20, once again, the even rate code. And then the next one would be x plus x plus 1, which would have to be 19. And then you have two possibilities for 3, right? You can have x plus 1 times, x plus x plus 1, which would give you 18 or what? Yeah, you can have several possibilities. M3 of x can also have M9 of x. Okay? You can have M3 of x and M9 of x. And then, okay, so I'm not going to write down the polynomial, sir. I'm just going to find out what k is possible. Okay, I'll ask you what k is possible. Let's see if any k is not there. What about 17? Is it possible? Yes. Okay, degree 4 is possible, right? Degree 5 is possible. Degree 6 is possible. Degree 7 is possible. Degree 8 is possible. Degree 9 is possible. Degree 10 is possible. 11 is possible, right? 12 is also possible. So it looks like for all dimensions you have it. It's enough if you check up to like 10. 10, 11 maybe. Okay, 10 is enough. It's enough if you check up to 10. If you see degree 10 is possible, x bar n plus 1 by that will give you the other degree. Okay, so anyway, so we'll all be okay. So it's enough. So all k's are possible. Seems like an interesting problem or not. I haven't seen it first anywhere. Maybe it is solved already. I have no idea. So what n, right? Let's ask the questions. Of course we ask the questions. For what n, do you have cyclic codes for all k's? Okay, I don't know if that problem is solved or not. I don't even know if this is nice enough problem. But it seems like an interesting enough problem that has come up in our computation. So it seems crazy, right? 9 doesn't have something and then 21 seems to have everything. So maybe there is some nice property that things have to be satisfied for you to get. Just think about it. If you come up with an answer, let me know. I don't think anybody else will be interested in it, but at least I am interested. So it seems like a curiously problem. Okay, so you can do this for other n also. Any other n also you can do this. So notice, I never have to go through any trouble of finding any which field in which there is a primitive 21st rule of unity, et cetera, et cetera. Nothing you have to do. You just have to do very simple stuff and this is the answer. Okay, so maybe we can try some other curious numbers. So let's try one more curious kind of number. Maybe we'll try n equals, let's pick a prime number. So let's say 17. This is for fun, right? 17 is not such a bad number as you might think. There are some things nice about it. So where will you find a primitive 17th rule of unity? So the numbers of the form 2 power n plus 1 is very easy to find the answer, right? 2 power n plus 1 times 2 power m minus 1 is the same as 2 power 2m minus 1. So once you find a number like that, it's very easy to find. So in fact, 256 will be the field in which you'll have. Okay, so that's some things you can use if you like. So this is not such a bad number. Okay, let's try the such a bad number. 1, 2, 4, 8, 16, what? 15, 13, 9, that's all. It cannot be more than 8. Okay, that's a good number. Okay, and then 3, 6. Okay, all the remaining has to come. I think that we could be 4 also. So we should be careful. 3, 6, 12, 7, 14, 11, 5, 10. That's it. Okay, so you have very simple looking factorization. So we have unknown effects and three effects. And then there are very few cases that are possible. So in fact, this number of cases that are possible, we'll have, of course, 17, then we have 16. And then what? 9. 9, no, 9. 9, 8. 8. That's it. And 1. Okay, 1, of course, you should have. 17 is there. 2 also should be possible. No, no, no, 1. Only 1 is possible. And 0, I mean, usually people use a trivial 0. K equals 0 means what? The null code. It's called nothing. I think all 0 code would be okay. You can take just the all 0 code. Okay, so that's really defined to have. No, it's no information. Well, let's try one more. What's the fun? Okay, I'm curious about what will happen. I have no idea. 90. It's a number. I have no idea. It's a time that will have 19. So one answer that's very easy is 19 itself. So 2 by 19 minus 1. 19 is a prime number. So 19 will divide 2 by 19. Let's try more. Yes? Okay, think about it. It's a result. Okay. So the way to find it is you have to count the number of numbers below n which are relatively prime to n. Okay? So 2 for that number minus 1. n will always be like that. Remember this rule. It's called so much little theorem. It's not a very difficult thing. 2 plus p minus 1. Yeah, I mean yeah, p minus 1. Yeah, it's 2 power 18. Okay, so you have to find the numbers that are less than 19 which are relatively prime to n. So 1 to 18, you have 18 of them. So 2 power 18 minus 1 will divide it. So up to 18 is fine. But then you can also have smaller factors. Let's check if 19 is such a bad number. It might just have one factor. So we'll see. Okay? So then you have to just multiply and check this, right? So 1, 2, 4, 8, 16, 14, 7. No. 7, right? And then 14, 9, 18. Oh yeah, it's bad. If 18 comes in the ninth position, right? Then everything else will also come. Okay, how do I know that? Minus 1, minus 1, minus 1, minus 1. Yeah, so all the minuses will come after this. Just think about why I said that. So that's how it starts to work out this way. So all the minuses of these pairs will come and you'll get just one. Okay, so 19 is a very bad number for cyclic codes. So you have just the trivial cyclic code. Okay? And you have only the trivial cyclic code. You have the identity and the all-zero. And then you have even rate and repetition. Okay? That's all. Nothing more to find. Is that right? Did I make a mistake? Okay. Okay, so what are the weird numbers in which strange things can happen? Usually prime numbers are a bit weird. Some things like this can happen. And usually in prime numbers. Okay? Let's see if we can take a nice example. It's about whether a module 4 or something happens or not. Anyway, it doesn't matter. Okay, so these are factoring experiments. Plus one, you can have a lot of fun with it. In fact, a lot of interesting questions can be asked around this factoring. You might think it's very silly, but there's very interesting number theory that can come into play. Okay? If the atomic process, when will they recover? It's an interesting little number theoretic problem. Okay? I think that's a solution. It's not very unsolved. I think it's an interesting really question that all of us can have a lot of fun. Since you asked me to do this in detail, so final exam becomes more interesting. So it's not when you have a choice, you have to exercise it very carefully. You don't have to do it carefully. I'm going to prep you like this. Okay, so that's about factoring. So factoring gives you all the ideas. So the next thing that is usually done is the dual term. Okay? So anyway, so let's not worry about the dual term now. The next thing that people talk about are zeros of the people. Okay? So we know that experiment plus one factors into linear factors and df to parent. Okay? So again, remember we'll take n to be odd always. Oh, I want to repeat this again. Okay? So for a cyclic probe, it's been defined by a generator polynomial, g of x, and this g of x divides x parent plus one. So what should happen to g of x also? g of x will also factor into linear factors into linear factors in g of to parent. Another way we are putting it is all the roots, g of x has degree r, it will have r distinct roots in g of to parent. So it's another way of expressing the same things. Okay? Has, so the first word degree is equal to r. Okay? g of x has r distinct roots in g of to parent. Okay? This is the other way. So when people say zeros of a cyclic probe, basically they're referring to these r distinct roots. Okay? So zeros of the cyclic probe set of r, let me say r, the set of distinct roots of g of x. Okay? This is a general enough definition. The distinct roots of g of x are the zeros of the cyclic probe. Okay? So, so a lot of times people just, they'll just put up the zeros of the cyclic probe. It's enough if you put up the zeros of the cyclic probe. Remember again, zeros of the cyclic probe. Okay? So, so one more thing we know is that the zeros of the cyclic probe, whatever's going there. So you remember? Yeah. The, the cyclic probe across it, yeah. All that will come before that. Even though it is in g of to parent, I know that the roots of x parent plus one are all powers of the primitive nth root of unity. Okay? So you only have to look at the element of g of to parent which has order n. Okay? So you know it cannot be an arbitrary, so the roots cannot be arbitrary elements of g of to parent. Roots will have to be powers of a primitive nth root of unity. Okay? So all the elements that are roots of x parent plus one will also have order dividing n. Okay? So that is also true. Okay? They'll all be exactly, can be written down as a powers of, is a powers of an element of order what? Of order n. Okay? So let me ask you another question here. Okay? Since you know x parent plus one cannot have more than n roots. Okay? So the other question I wanted to ask is, can there be two elements of order n then? Two different elements of order n in g of to parent. Is that possible? Can there be two different elements? Okay? But then if there are two elements like that, one should be written, one should be, you should be able to write one as power of another element. Okay? Why is that true? Okay? If there are two elements of g of to parent which both have order n, then you should definitely be able to write one as the power of the other one. Why is that true? Yeah, there's one that has to generate everything. Well, x parent plus one cannot have more than n roots in g of to parent. It has to have only n roots. Right? So when you write up all the powers of an element of order n, that should give you all the roots of g of to parent plus one. You cannot have any other root which cannot be written as a power. Okay? There can be more than one element of order n. Okay? So you take the primitive entropy of unity and raise it to a power which is relatively prime to n. Then you will get another element of order n that's it. Okay? But it's all expressible as the powers of each other. Okay? The same result as saying every, every field has only one primitive element. What? Not one primitive element. Can I have multiple primitive elements? Then you can always write one as the power of the other. Okay? So it's always possible. You cannot do anything. Again and again and again to prove these kinds of results. Okay? Anyway, so the distinct roots of g of x are there are zeros of the cyclic code and usually people use the zeros to define the cyclic code. They say consider the cyclic code with zero set. This is the set of zeros. But that fully fits the cyclic code. Okay? And so look at the check polynomial. So we define something called the check polynomial. Right? So before that I should point out also the other thing. The roots of g of x have to be union of cyclic atomic process. Okay? So that's the first time. The roots are, let me say zeros. Zero of r. Elements of. Other. Dividing n in g of 2 of r. Okay? So zeros are, let me say r, what I mean is, you see what I mean. So it cannot be an added element. Only those elements whose order divides n can be a zero of a cyclic code. Okay? That looks true. The other point is zeros will be, zeros are unions of cyclic atomic process. Why should they be unions of cyclic atomic process? Otherwise, the factor will not be binary. Okay? So if you have one zero from a cyclic atomic process, all the other zeros will also come separate. You have to take, you cannot drop. Right? So otherwise, the thing will not be binary. Okay? So what people will do is, when they specify zeros of a binary cyclic code, they only specify one from each cyclic atomic process. Just to simplify the notation a little bit. So you say, okay, it has the cyclic atomic process, the cyclic atomic process. Only provide the representative. That's enough. Okay? We don't have to keep listing all the zeros in full very detailed because we know all the other cyclic atomic process. Elements will come anyway. Okay? So these two ideas are used quite often. They need to find cyclic codes. And then what else? So, okay, you can move on to the check polynomial. So there's something called the check polynomial. This is again interesting. It is the property of the check polynomial. So basically, we define check polynomial as the perfect to be x bar n plus one divided by gfx. Okay? So it's a product polynomial. It's also as active as x bar n plus one. Okay? So basically it divides x bar n plus one also. So one nice property is, cfx belongs to the cyclic code. Which one of these? Cfx times hfx equals zero in rn. Okay? So this is the main result, which is nice about the check polynomial. So one direction is very easy. The other direction is also not too bad. So at cfx times hfx being zero in rn, cfx times hfx should be some multiple of x bar n plus one. And then from there, you can quickly decide that cfx will have to be a multiple of gfx. So which fx divides x bar n plus one, you take it to the other side, you get gfx. So gfx has to divide cfx, and that's why cfx is a code one. Okay? So both directions are easy to prove here. It's not very hard. Is it okay? Okay? So see, remember how we proved this? cfx is the sum mfx times gfx. So what will happen if I do cfx times hfx? I'll get mfx times gfx times hfx. What is gfx times hfx? x bar n plus one. So that has to become zero in rn. Okay? The other way you say, cfx times gfx is actually mfx times some efx times x bar n plus one. We derived the hfx. We'll get efx times gfx, and that tells you cfx is a code one. So you can prove it just based on these properties. What is nice about the Czech polynomial is it has a zero set which is the complement of the zero set of the code. Seriously, zero sets of Czech polynomials. So cfx is zero one minus one, and you do a set minus with those zeroes of the code. Okay? That's one thing. The other thing is the Czech polynomial by itself also defines another cyclic code. You can also think of this cyclic code. Okay? But we'll have zeroes given by this. Okay? And this cyclic code and the original cyclic code have an interesting connection. So it's not a very obvious kind of connection. So that needs a little bit of more work, and that's where the dual comes in. Okay? So it turns out to take this hfx, and you have to do a reversal, to do the reversal. That will also be a factor of x bar n plus one, and that will generate the dual code. Okay? So those are things I think I proved. So I'm going to just write down the result here. So one can show that the dual of the cyclic code is, again, a cyclic code. Okay? So if you have c being a cyclic code, okay? And the c is equal to gfx. Okay? You define hfx to be x bar n plus one by gfx. Okay? And then you do the following. You define something called hfx, which is x power bgfhfx times hfx inverse. Okay? So this is something I did when I needed the dual. So I'm not going to prove this result for you. Okay? I'm not able to go to the next page. So I'm not going to prove this result for you. So first of all, hfx will also derive x bar n plus one. How do I prove that result? hfx divides x bar n plus one. Okay? Okay? So you use the fact that x bar n plus one is gfx times hfx. And then multiply both sides by x bar. Good? x equals x inverse in both sides. So you get x bar minus n plus one. gfx inverse, hfx inverse. And then you multiply both sides by x bar n. Okay? So we'll get one plus x bar n back again on the left-hand side. On the right-hand side, you split the n as degree of gfx plus degree of hfx. And take x bar degree of gfx into the gfx inverse. And x bar degree of hfx into hfx inverse. Both of them will become proper polynomials.  So this is the way. The second thing is, more interesting with all this, c bar is this square cyclic code generated by hfx. Okay? So this is the result I showed before. So I'm not going to re-prove this for you. But this is how it works. Okay? So now how do I find zeroes of the real code? Okay? So I'll go z equals zeroes of zeroes of zeroes of c What is the zeroes of the real? It'll be what? Negative of the complement model. Right? So you have to first take zero one two n minus one z minus z. And then what? It'll do. So suppose I call this that complement. Okay? And then I have to do minus z complement. Of course you can do modular one. Or you can just stop with minus z complement and then understanding that it's everything is modular. This is the zeroes of the real code. Okay? How did I get that answer? What I'm doing is hfx inverse. Okay? So all the roots will become inverses of each other. This is minus. In terms of powers it's minus. So this is the main result. It's just interesting. The dual has minus z complement model. Okay? So I'll put up from here on Tuesday. Okay? And I will start working on it. Okay?


Thank you, John. It is a pleasure to be here. As John said, I was here a few years ago lecturing on the Portsmouth Naval Shipyard during World War II. But some background for this book, Whips to Walls, a few years ago as a 68-year-old graduate student at the University of New Hampshire, I found myself, it's not funny. Not only was I older than all the students and all the professors, I was older than the fathers of the professors in most cases. But I found myself at the archives in Waltham, Massachusetts researching for a dissertation which eventually turned into that 32 and 44 book. And while I was there, I kept stumbling across references to a Thomas Mott Osborne, who was the warden at Portsmouth Naval Prison during World War I. And as it turns out, Osborne is credited with conducting the most ambitious experiment in progressive prison reform. And when I say progressive prison reform, think open cells and prisoners guarding prisoners. But the most ambitious experiment in progressive prison reform ever, anywhere. And so after I got done with 32 and 44, I decided that I'd go back and do some more research on Osborne and write a book on him. And it so often happens when you start out with a book of very limited scope, why that eventually got expanded not only from the Portsmouth Prison during World War I, but back to the origin of the prison in 1908. And then back to the origin of the Naval Prison system in the late 1880s, and then back to the abolishment of flogging in 1850. And the theme of the book and the theme of the presentation today is the Navy's journey from a very harsh punishment system in the mid-19th century to one of the most lenient of punishment systems at Portsmouth Prison during World War I. And there were a number of bumps in that journey that we'll discuss today. So we'll go from flogging in 1850 to the Portsmouth Naval Prison during World War I. And as I drove down here, I came through Portsmouth Rhode Island, so I thought why better explain that the Portsmouth Prison I'm talking about is in New Hampshire, and not one that happens to be up the road in Portsmouth Rhode Island. But those of you who aren't familiar with the prison, and I learned during the setup that my laser doesn't really work on this background here, so I'll be pointing at things. So those of you that aren't familiar with the prison, it's on the Naval Shipyard, which is on this island in the Piscatical River between New Hampshire and Kittry, Maine. The prison has been closed since 1973. It's been vacant, inhabited only by bats and rats and miscellaneous other creatures, and it's gradually deteriorating. But it's going to be a long time before that structure falls down because it's a very formidable one. But as you can see, the only way you could get land access to the prison is by coming through the main gate or the other gate here and transiting the entire length of the shipyard. So the Navy is continuously trying to find a client for that building. But just the access to it is so difficult, and then it's laden with asbestos and lead paint and all sorts of other environmental hazards. So it's not going to have an occupant any time in the near future. But that's the background for the prison. This is a close-up of it. It really does, it's a tourist curiosity. It draws a lot of attention to anybody that is driving by Portsmouth. And the prison that we'll be talking about during World War I is this wing and this tower. That was the original prison. These other buildings were constructed during World War II. So I like to use this chart to highlight the lecture for today and really for the book too. And I depict the naval discipline as a pendulum going from a very harsh punishment over here in the early 1850s to Osborne at Portsmouth. And as you can see, the pendulum started moving to the left with the abolishment of flogging in 1850. And then the Navy was left with a discipline void. And I'll get into this. But flogging was a very efficient punishment. And when that was abolished, why COs really didn't have other options at sea, to confine a sailor at sea was very difficult. There were no prisons and there wasn't much liberty and there was very little pay. So what was a CO supposed to do? They were really left with a discipline void. So the pendulum gradually swings to the left. The graugration here was abolished in 1862. That was a source of a lot of the Navy's discipline problems. So that helped. And then in the mid-1870s, the Navy attempted to get Congress to fund a prison for them. The Army was successful getting Fort Leavenworth funded and it was built in the early 1870s. So the Navy thought they might get their own prison. Congress wasn't about to fund a naval prison at that point. And the Navy was sort of told to go away. And what they did is they developed their own makeshift prisons at Boston and Mary Island. They used an old granite warehouse at Boston Naval Shipyard and turned it into a prison. And at Mary Island, they had a Marine Corps barracks jailhouse that they eventually turned into a prison. So they were makeshift prisons. And all of this, well then in Portsmouth prison, when these weren't working out too well, Portsmouth was built in 1908. And all of this was done under the influence of the progressive movement in the late 1800s. The progressive movement was taking increasing awareness of the poor and the unfortunate. And that's also included prisoners. And Thomas Mott Osborne was very much a product of the progressive movement. And so under the influence and the strong support from the Assistant Secretary of the Navy, Jofeces Daniels, and the Assistant Secretary of the Navy, Franklin Delano Roosevelt, Osborne was installed at Portsmouth prison in 1917. And we'll get into that in quite a bit of detail. But it so often happens when Osborne was replaced in 1920, why all of his liberal reforms were done away with and there was an instant backlash. And the Navy discipline pendulum started back in the other direction. So going from flogging, flogging was, as I said, a very efficient punishment for the Navy. And it was needed because the seamen at that time were really a group of ruffians. They were more than likely foreigners. They liked their grog ration and an occasional riot assure. And so it took a very harsh discipline system to keep that that group in line. There were various forms of flogging that shows the seamen being bent over a cannon and administered his lashes. The lashes were administered with the cat and nine tails. And supposedly, the maximum number of lashes that could be prescribed were 12, if you were a commanding officer, and 100, if you were guilty of an offense that required a court marshal. Now the most common punishment, and I did a lot of research on this, was 12 lashes. That was sort of a one size fits all punishment. But there were extremes. If there happened to be a number of ships in a harbor, they had a routine that was called round the fleet, where they just passed the sailor, the seamen from boat to boat. And there are some extreme examples where a sailor might get 300 lashes. You know, the Navy regs were there, but they weren't very well enforced. Now it's hard to work humor into a lecture about prisons and flogging, but I did find this cartoon of the mastered arms bringing a cat with nine tails up topside in preparation for the flogging. So the argument for flogging, as I said a couple of times, were very efficient and very effective. And this is one officer's view of the need for flogging. And my wife is here and she doesn't allow me to put up slides that have a lot of reading on them, but sometimes that's hard to avoid. So I do have a couple. One officer's view of flogging in 1840. Extra labor, ordinary confinement, solitary confinement, bread and water diet are plans that do not suit well on ship board. Solitary confinement is not practicable on board ship. From the one of room, if cells were built in the hold for the purpose, they would take up space required for storage. Every man should be at all times at his post. This end would not be gained by throwing offenders into confinement. So as I indicated in that opening slide, there really was a void in the Navy as far as discipline was concerned with the abolishment of flogging. So in the late 1840s, Congress was trying to get around to abolishing flogging and they tried to build up their database to support that. So COs were required on a number of occasions to report the floggings on their ship back to Congress. And this is one flogging report that that I went over among several. It involved 14 ships over two and a half months in 1848. And as you can see, there were a total 446 floggings. So if you go back and do the math, that was something like 32 floggings of ship. Every other day, somebody was getting flogged on a ship on one of these 14 ships. And for what? Most often drunkenness. And all of these other offenses, which often were a subset of drunkenness. So the the Daily Grog and the Navy was certainly a big problem. But those were the type of offenses. And as I said, the seaman at the time was a rather rough individual, and it took flogging to keep him in line. Now flogging was abolished in 1850. These two gentlemen, and this is a popular slide in Portsmouth, New Hampshire, where I've given this a couple times, because a couple Portsmouth lawyers were very much involved with getting flogging abolished. The first Levi Woodbury was a Portsmouth lawyer, later a governor and senator, but it was his secretary of the Navy in 1831 that he initiated the earliest attempts at getting flogging absolved. But he also offered in a directive, he offered the seaman a chance to give up their grog ration for pay. He would increase their pay if they gave up their grog ration. It was not very well received at all. As it turns out, well not just because they liked their grog, but as it turned out for the very minimal offenses, their grog ration could be taken away. So the seaman felt it was better to have a grog ration that might be taken away than the next step up, which would be a flogging topside. So Woodbury's suggestion there didn't get very far. However in the late 1840s, John Hale, who again was a representative of New Hampshire and a senator, he introduced the first bill to abolish flogging in 1843. It didn't get very far. But then in 1850 there was an appropriations bill that somehow he tagged the abolishment of flogging onto this appropriations bill and it passed by two votes. It was almost like all of the northern congressmen voted for the abolishment of flogging and all of the southern congressmen didn't. But under the influence of these two men, why flogging was abolished in 1850. Now the abolishment of flogging left the Navy with insufficient penalties to enforce discipline. And here's one of the slides I used to put up that I'm not allowed to read to you, but let me go over this. The abolishment of flogging left the Navy with few options and there was a board put together under Commodore Charles Stort in 1851 to study the effect of the abolishments of flogging. And this is what his report had to say. We are therefore in our opinion without sufficient suitable penalties to enforce discipline of the Navy. Another one, strictly speaking no summary punishment can be inflicted by a commander of a ship of war at sea. And finally it cannot be doubted that the law in its present shape is insufficient and unsuited the service. So they were left with a big problem. And as I said there was very little pay, very little liberty and shipboard confinement was not effective at all. And discipline was inconsistently applied through the fleet. Punishments were suggested but really they were invoked according to the personal whims and prejudices of the COs. Yeah, something makes me think I should be reading, yeah. As far as the COs go, this is what the COs had to say about confinement in 1851. Confinement is a trifling punishment. While they the prisoners enjoy a respite from work, innocent men actually suffer by having the onus of duty imposed upon them. Another, I have tried all kinds of punishment and I feel at my duty to state that I do not think discipline can be maintained in our service unless by flogging. The attached punishment row is small because in vessels of our tonnage well at sea we could not spare the men from deck and I have therefore been obliged to let many offenders pass unpunished. There's no place on a ship of war where a man can be confined for punishment without seriously injuring his health. So the COs were sort of at their wits end in 1851 with the abolishment of flogging. Now the book is filled with examples of this next issue about the inconsistent invoking of punishments and I've just picked this one example to show you. But if you happen to be on the monocacy in 1867 and you smuggled liquor on board, you were confined in double irons for 10 days, you lost pay for five months, and you lost your liberty for one year. If you happen to be on the Shenandoah, they put you in irons for 48 hours. That's how inconsistent the punishments were in the fleet. However on the Shenandoah which happened to be in Japan at the time, for the punishment for furiously fighting and killing the Japanese, that was also double irons for 48 hours. So it was just all over the board. There was no consistency whatsoever. And not only couldn't you confine a seaman very effectively at sea, there were a very limited number of shore confinement cells. They had prison ships, they had Marine Corps barrick jails, they had Navy Yard jailhouses, but it was just a potpourri of confinement facilities. They really needed a prison. Neville Discipline was chaotic, cells sure were limited and scattered. A prison system was vitally needed. So let me take you through this. One of the hazards of training an engineer to be an historian, I was an engineering duty officer, is that you end up with a lot of graphs and tables in your history books. And I've tried to cut back on the number for this presentation, but there are a few. This shows the green is the number of enlisted personnel in the Navy and the Marine Corps between 1880 and 1939. The red is the number of Marines, the blue, the number of enlisted sailors. So what I want to show you here is back in 1875, when the Navy was first denied funding for a prison, Congress really wasn't even funding a Navy at that time. They weren't about to build a prison. So this goes along, and then in 1888, the Navy developed a need for a prison and they built the two makeshift prisons at Boston and Maryland. Camp Long, this was a Spanish prisoner or war camp on Seve Island in Portsmouth, New Hampshire, the exact site where the Portsmouth prison stands now. So on the chart, this little bump here is for the Spanish American War. And Admiral Savera, on July 3rd, 1898, I think it was, was defeated at the Battle of Santiago. And like three, four weeks later, there were a couple thousand Spanish prisoners on Seve Island. And turns out it was a very successful prisoner or war camp, and that led the Navy to believe that maybe we ought to put a prison there. Portsmouth prison was built in 1908. As you can see, we're ramping up. And then there's this big boom for World War I, and that's when this Thomas Mott Osborne was at the Portsmouth prison. Now, you might say that the population of the Navy and the Marine Corps isn't necessary a reason for an increased need for prison cells, but actually the desertion rate in the Navy and Marine Corps was pretty consistent at about 10% through that whole period. And that was the prime need for prison cells. So this is the Boston prison, a converted storehouse on the shipyard that was made into a prison in 1888. I took that prison or picture myself just a few years ago for those of you that haven't been up to the Boston shipyard since they closed it and have renovated. It's just a beautiful area now. And so this prison is now a very attractive office building with a plaque that commemorates its proud history of a naval prison at one time. The Maryland prison, this little structure here was the original prison that was built back in the early 1870s. And then both prisons struggled to keep up with the need for cells. And so the Boston prison expanded upward to the floors above and they built wings onto the Maryland prison. Just this week I was telling John that I've been working with the Historical Society in Vallejo, California. A developer has bought the land where the Maryland shipyard was and now he wants to develop it. And the Heritage Commission out there is trying to save the original prison.  And they are trying to save it. The Camp Long that I mentioned about on Seve Island, the site of the future prison, there were 1600 Spanish prisoners treated well. You read through the archives and you just can't believe that we treated prisoners of war so well. The prisoners gained 10 or 15 pounds during the two months that they were at Camp Long. Officers had wine served at the mess. The hospitalized prisoners and there's a hospital right next to the prison up there why the women of Portsmouth and Kittrie, Maine would come in with flowers and cigarettes for the prisoners that were in the hospital. And as I mentioned, Admiral Severa actually got out and walked the streets of Portsmouth. This is a picture of him wandering around the streets of Portsmouth, New Hampshire in August of 1898. These are prisoners bathing in the Piscata River and being well treated. Now I mentioned that the experience at this prison Camp Long was so positive that it induced and enthused the Navy about building a prison on Seve Island. The prisoners were there in July and August. Had the prisoners been in there December through February, they might not have been as enthused about building the prison on Seve Island. But after that experience, as I mentioned, the Boston prison had been overloaded so they put a prison ship the Southry in Portsmouth at the site where they were in the process of building the prison. And I found this post, John, what did I do? Ah, okay. I like the old days when you had a flip chart or a projector. And as long as you had another bulb why everything was okay, these things are a little scary. But this was a postcard. What it is showing in 1905, in July of 1905, the biggest TNT explosion up to that time occurred to blow a point of land off of the shipyard here, Henderson Point, to increase the navigation of the Piscata River. But I just show you here that this postcard from 1905, this is the prison in the background. They started to build it in 1903. In 1905, it looks like it's done, but it wasn't open until 1908 because they had trouble getting funding for it between 1905 and 1908. This is what it looked like in 1908, as I mentioned, just the main tower and the one wing. But the Navy finally got a real prison in 1908. The one in the real prison because the two they had in Boston and in Mary Island really weren't that intimidating. And this Alcatraz-like structure is really an intimidating prison for those of you that weren't there. Now, this is a postcard that one of the historians up at Portsmouth passed on to me. You can't read it there, but there was a young man from Western Pennsylvania who was a prisoner at the prison in 1910. And he's writing his parents back in Allegheny County, Pennsylvania. And he's talking about getting home for Christmas. And the only reason I put this up is I mentioned the need for flogging because the seamen back in the early 19th century were such a group of ruffians and drunkards and foreigners and really tough. By 1910, the seamen had changed. There was a lot more recruitment in the Navy from the Midwest. And you were getting a lot of young men into the Navy who really didn't understand what they were getting into. And more than likely, they were running a file of Navy regulations. And so they were at the prison for having violated some Navy regulation offense. The really hardcore criminals were moved then on through the prison into a state prison. And the President Concord, New Hampshire did have a lot of the hardened criminals. Now, about this time, I've got you up to the 1913 timeframe, President Wilson and the Progressives moved into power. As it turns out, after Andrew Johnson was impeached about the end of the Civil War, eight of the nine presidents prior to Wilson were Republicans. One of them, Rover Cleveland, had two terms that were separated. And when Wilson came to power, the Republicans had been in power for the last 16 years. And really the only reason the Progressives got in was because Taft had been president. And then Teddy Roosevelt wanted to run against him on the Boom Moose Party. And so they split the vote. And Wilson got in. But the Progressives were very enthused about having regained the presidency. And this is a picture of Wilson's cabinet. This is Wilson. This is William Jenny Bryant, Secretary of State. Three times ran as a populist candidate for president, was an avowed pacifist. And he actually resigned to Secretary of the State after the Lusitania was sunk. And Wilson had no choice but to start moving towards war. He resigned. This is Jofeces Daniels, just his heads there. But a lot of the Naval officers suspected of him of being a pacifist too. This is Wilson. This is FDR standing over there. So the prime personalities now for the rest of the lecture and the rest of the book are Jofeces Daniels, FDR, and Thomas Mott Osborne. Jofeces Daniels had absolutely no previous naval experience, had been a newspaper editor for the Raleigh Observer down in North Carolina. He was a fixture in a Democratic party and had helped Wilson get elected. So his assignment as Secretary of Navy was reward for that. He was a strong prohibitionist and celebrated when the prohibition era started, I guess. He was enlisted men's champion. He had many disagreements with naval officers. You might remember that it was his general order in 99 that abolished the wine mess on the ships. He wasn't too popular with that. He tried to change, I'm told, Porton Starbert to left and right. He was a problem. As John mentioned, he had some issues with Admiral Sims. That is not an understatement. I found these cartoons. Here's a picture of Daniels roasting Sims over a fire. Here's a picture of Sims shooting holes in Daniels war record. Now, there were a number of issues between Sims and other senior naval officers and Daniels, not the least of which, as it turned out, Sims accused Daniels of avoiding preparations for war in World War I. Wilson campaigned under the heading of he kept us out of war. So Sims maintained that Daniels put off the Navy's preparations for war in order to get Wilson re-elected. As a result of that delay, tens or hundreds of thousands of lives were lost and billions of dollars were expended. This turned into eventually a congressional inquiry and it was really a big deal. But the point I want to make here is that there were a number of issues between Josephus Daniels and the senior naval officers in Portsmouth prison and Thomas Mott Osborn was really a subset of that whole environment. Franklin Delano Roosevelt. I like to show this because we usually see pictures of him struggling to get up to the podium or in his wheelchair. In this timeframe, he was a very young, a very energetic, a very ambitious, a very handsome, a very athletic individual. He graduated from Harvard in 1903, married Eleanor in 1905. He was a New York state senator from 1910 to 1913 and that's the connection between he and Osborn. Osborn was also into New York politics. They both fought Tammany Hall and that's where their relationship started. He ended up being a VP candidate in 1920, which is the tail end of the era that we're talking about. So, another one of my graphs, but I've gotten you up to the 1913-1914 timeframe and now I'm going to take you through 1920. What this shows is where the naval prisoners were confined between 1940 and 1920. At your choice of Portsmouth, that prison ship to Southry, Perilis Island, the Mayor Island or the Cavite prison, the Boston prison was closed in 1913. But I draw your attention to the fact that Portsmouth and Southry here dominate this whole chart and the message being that if Daniels and FDR and the progressives really wanted to implement a progressive prison reform program, there's no doubt that Portsmouth was the place to do it and that's what they did. They brought in this guy, Thomas Mott Osborn. He came from a family of abolitionists, women right activists, and as I said earlier, he was really a product of the progressive era. He was a New York politician. He had been the warden at Sing Sing Prison immediately prior to coming to Portsmouth. At Sing Sing, he left amidst a bunch of scandals and problems with the senior politicians in the state, including the Governor. There were accusations of rampant homosexuality at the prison, poor prison administration. He really left under a cloud. But he was a prison reformer and Roosevelt knew him, and that was his link to Portsmouth. They made him a Lieutenant Commander in the United States Navy. He didn't even know what the Navy was, and Daniels and FDR made him a Lieutenant Commander in the United States Navy. He was 62 years old, so he was older than the commandant at the shipyard. He was probably twice as old as the Lieutenant Commanders and he thought he knew more than all of them put together. He had that type of a personality. So here you got this 62-year-old Lieutenant Commander at Portsmouth Prison running things and he's always wanted to run his own show. He was a weird duck. He loved disguises. Before he became the warden at Sing Sing Prison, he went in in prisoner's garb just to see what was going on. He did the same thing with another gentleman at the Portsmouth Prison before he took over there. And there were other instances in his background where he did that. This shows him demonstrating a head cage while he was warden at prison. He went to see, as Seaman Brown, just to see what a sailor's life was at sea. And if you can read this, this is a picture that was sent to Jonathan Daniels. Jonathan Daniels was the son of Jofeces Daniels. That's the close link that they had. Osborn loved disguises. He was buried in a Portsmouth Prisoner's uniform. When he died in Albany, the suburb of Albany, New York, he had been to attend a theater performance where his son was in and he wanted to go into skies. And he had whiskers and some things in his cheeks to puff out. And he died on the street and people didn't know who he was. It took him a couple days to sort out that that was Thomas Mott Osborn. But that's the strange duck that he was. And just to build on this a little, he was the head of the hasty Pudding Club at Harvard when he was there. When he was at the Portsmouth Prison, he started a theater group and they made presentations. He would get permission from Daniels or FDR for this group of prisoners to leave the shipyard and perform in Portsmouth or York, Maine or over in Manchester, New Hampshire. And this is just for 1999 or 1919 where these groups performed at the Portsmouth Music Hall several times, York, and then over in Manchester on one occasion. So another graph. But to make this point, this shows prisoners at the prison restored, received dishonorably discharged. What I want to draw your attention to is this one, restored to the Navy. Prior to Osborn's arrival, there were almost no restorations. After Osborn's departure, there were almost no restorations. While he was there, there were a phenomenal number of restorations of sailors returned to the fleet. He was the prisoner's champion and the commandant's nightmare. His administration for the prison was known as the Mutual Welfare League. And as I indicated earlier, prisoners guarded prisoners. They did away with marine guards. They had prisoner judges and juries. They had open cells. It was just the most liberal prison environment you could possibly imagine. He had started this concept at the Sing Sing prison and it got him in trouble there and that carried over to Portsmouth prison. For one thing, he refused to separate prisoners. Navy rigs required that if a prisoner came to the Naval prison and he was guilty of a criminal offense, robbery, murder, assault, why he was to be separated from all those prisoners that were guilty of military offenses. And more than likely, the criminals then would pass on and go over to the state prison. Osborn was the mind that any prisoner that came to his prison started out on an equal footing and they could earn privileges as a result of their good behavior at his prison. And that wasn't what Navy rigs said, but that's the way Osborn ran his prison and that got him in the trouble too. And as I mentioned, he formed theater groups. As far as the commandant was concerned, and I've spent a lot of time in shipyards and I just can't imagine the disruptive force that this guy must have been in a shipyard where you were trying to build ships and submarines and repair war damage during World War One. He had absolutely no respect for the chain of command. He used his personal relationships with Daniels and FDR to work around the commandant and anybody else in his way in the chain of command. I found that at least during his period that he was at the prison, which was like two and a half years or so, he made six visits to Washington D.C. as a lieutenant commander to personally talk to the assistant secretary of the Navy or the assistant secretary of the Navy on problems that he had. So he had no respect for the change of command, no use for naval customers and traditions, and he just caused endless in-yard disputes. For example, and I found all of this in the archives at Waltham, I found memorandums between Osborn and the commandant where Osborn was asking that his prisoners be given rifles so that they could conduct drills so that when they were restored they'd be ready to go back into the fleet and serve a good purpose. Now, he did have a PS that said we would take the firing pins out of the rifles, which I guess satisfied the commandant a little, but just the fact that he might request rifles. There were other examples where it was hot in the shipyard and he requested that his prisoners not be required to work if the temperature was above 90 degrees. On other occasions, he defended a prisoner's refusal to work in the rain and these work parties that were out in the shipyard were just a source of endless debates and not the least of which was Osborn absolutely despised the yard Marines that were initially there to guard the prisoners and there was no end of disputes between he and the Marine officer on the base. He was also an irritant to the fleet because too many marginal sailors were being returned to the fleet. Admiral's would write him letters asking him to solve a problem and these would be a short two paragraph letter and the Admiral's would get a four or five page letter back explaining to them why they were wrong and that's generally not the way the Navy works so it caused a lot of irritation. Admiral Sims, his opinion of Portsmouth confinement. It was a nature of jest, a home so good prisoners would not even try to escape. Captain Tossig thought that fleet was being burdened with riffraff and immoral perverts and a rear Admiral Nimlach wrote some prisoners prefer Portsmouth to sea duty. So gradually this filtered up the line with all these admals asking what the heck is going on at Portsmouth prison and there was a JAG investigation conducted during the latter half of 1919. It started off as an investigation into a misappropriation of funds but as a JAG investigation went on it just became a horror story of homosexuality at the prison with the possible inclusion of Osborne himself and so Daniels had no choice but to assign an investigation board and FDR insisted himself that he had that board so he and two other admals in January investigated Osborne at Portsmouth prison and the report was that the previous JAG report, the board's report was that the previous JAG report was superficial and perfunctory. They absolved Osborne of all blame. They praised the conditions at the prison and that was in February. Make a note here that the Providence Journal down this way was really, couldn't have been more strongly anti-Daniels and anti-FDR and the editor John Ratham wrote often on the shortcomings of Daniels and FDR but he considered this board's report a total whitewash the culmination of political chicanery and Osborne resigned in March of 1920 just one month after the investigation concluded so he was absolved of all blame but he resigned. Now I usually don't have this slide in the presentation when I give it because I'm at the Newport Naval Station I thought I've included because it's included in the book but there was a sex scandal at the Newport Naval Station during these the same months that all this investigation was going on at Portsmouth. In December of 1919 there was a controversial investigation into homosexuality here at the Naval Station and Daniels and FDR were accused of condoning the entrapment plan that was put in effect to expose this this ring of homosexuals and as a result five Newport sailors were sentenced to Portsmouth for five to 30 years for homosexuality. Well this Ratham at the Providence Journal again that just put him all up in arms and he raised all sorts of issues to the point that Wilson directed another investigation of this investigation and once again he absolved Daniels and FDR of all blame and and Providence Journal considered it another whitewash. Now there was no end to this later this was in January 1920 about the summer of 1920 FDR resigned and then he ran as a vice president as a vice president candidate the rest of that year and this Newport sex scandal and the Portsmouth prison scandal were all they interrupted his campaign to say the least and then once Cox and FDR lost and the Harding administration moved in why the Republicans reopened that investigation into the Newport sex scandal and there was a different result the methods were considered most deplorable and disgraceful FDR's actions were considered most reprehensible got a lot of publicity at the time but really had gradually faded out except for the fact that in September of 1921 the five Newport sailors that were in the process of serving from five to 30 years at Portsmouth prison were released. I'm trying to create the environment of all this confusion and turmoil that existed between the Navy and Daniels and FDR during their tenure. In March of 1921 the Republicans regained the presidency under Warren Hardy Edwin Denby here relieved Daniels Denby enlisted into the Marine Corps when he was 42 years old he was married and he weighed 260 pounds and he had to have waivers for all three of those he entered as an enlisted man arose to be a major and so he's the guy that's replacing Daniels and the liberals so you might get the sense that whatever was going on at Portsmouth prison wasn't going to go on much longer under this X Marine and he appointed a Lieutenant Colonel Hamilton South as CO of the Portsmouth prison so as a earlier chart as soon as South got in everything with all the liberal reforms were thrown out he immediately abolished the mutual welfare league the theater groups were no more no more baseball teams none of that good stuff immediately increased guards police and the work parties consequences of misbehavior was absolutely and totally intolerant of homosexual prisoners and he resued reduced restorations to a trickle so the naval discipline pendulum that had swung from very severe to very lenient now started back in the other direction now this is just because i've been asked several times what happened after that this shows the populace no i'm sorry this shows prisoners restored during Osborne's tenure the percentages of so in 1919 over 50 percent almost 60 percent of the prisoners that were received at Portsmouth were returned to the fleet and as you saw a lot of the fleet officers considered that riffraff and moral perverts but i this sort of depicts the wave of progressive prison reform that swept through the prison at that time this is the chart that shows what happened at the prison uh after uh osborne left actually from 1929 to 48 you can see the this is the population uh at the prison the prisons prisoners confined the prison was just a shadow of its former self until the second world war when it took all these prisoners on board again years that long when the real the real long when there is 3000 nothing all the year on 1945 right at the end of the war so this is another book i don't have much details on that but but you can see that uh it resumed now what is important is during this period earlier i was showing you that that osborne had maybe a couple thousand prisoners there were more from the picture that i showed you earlier the prison was greatly expanded in world war two so they had far more prisoners confined there during world war two but they didn't restore anywhere near as many as osborne restored during uh during world war one so in summary the naval prison system evolved after flogging was abolished in 1850 uh port smith prison became the crown jewel of the naval prison system osborne's experiment at port smith prison during the war was the high water mark of progressive prison reform and it was the fleets disapproval of osborne's methods and restoration practices that resulted in an immediate backlash upon his departure departure so that's all i have for you yeah right on schedule this afternoon i'll take question yes sir i heard no mention of the use of bread water well you have to lay that out that was uh during that period that i mentioned where there was we're struggling to find uh other punishments after flogging i mentioned some of uh couple ships and irons there yeah they might be in irons on bread and water that was a pretty common punishment to say the least yes sir what is the facility of the archive and wall fan and the other one is this levi woodberry yes he was a senator and also secretary of the navy at the same time oh no no no he was governor he was a senator before he was secretary of the navy what did my was my slide confusing i'll go back and check that now your first question was in wall fame you said you got data what's the facility oh yeah it's it's the new england regional uh national archives it's a wealth of uh uh data not not just for the naval shipyard for for all of new england where in wall fame isn't well i know you go down 95 and get off and go a couple lights i'm not that familiar i'm not that familiar with uh with wall fam but uh just like everything if if you google nara national archives regional agency i think it is wall from massachusetts that uh it'll give you the address thank you yes sir impact of flogging uh did it create a wealth in the skin or did it kill the flesh did it kill the flesh yeah absolutely you could kill somebody flogging them they're uh now how they treated it i i don't know but i've seen some horrible drawings not pictures of uh the impact of flogging there's oh yes oh i i'm glad you asked that because i showed the cat of nine tails the cat of nine tails is really uh a whip with nine strands of leather with lead pallets embedded uh into the strands of leather so those hurt no no doubt about it yes sir flogging abolished in 1850 uh do you know if it was reinstated in the confederate navy i found nothing that indicated that it was reinstated in the confederate navy along those lines it was abolished in the u.s army in 1812 it took the navy many more years to get around to it it was abolished in the british navy uh before before we abolished it we were one of the last to abolish it yes sir did you come across any statistical data about flogging being abolished and then a spike in offenses punished you know they some of the uh quotes you had said you know it was tough to to deal with punishments or things are going on punished but did the loss of the deterrent actually increased the the answer is yes and i can't give you the date on it but i can give you one example there i can't remember the name of the ship but there was a mutiny as soon as the sailors found out that they couldn't be flogged anymore why they all deserted you know and i wish i could remember the name of the ship if i can't but but it uh there was no doubt that there were there were repercussions from it and i showed you the statements from the co's it's a hey we've lost control there's really nothing we can do i'm not even uh punishing offenders anymore because i've got no means to do it yes sir in the back that's true uh i can't attach any uh i haven't done the research i'd be guessing if i told you i don't honestly know about the confederate navy but the grogration when when a flogging was abolished in 1850 well i indicated to you that from as early as 1830 congress was trying to do something with the grogration and in 1850 when they abolished flogging there were initiatives then to do away with the grog but they thought that was really too much to lay on them at the same time so i don't think it was so much a matter of some champions coming forth to get the grogration absolved it's just the pressure finally built up and then when the civil war started they figured well okay we can do it at this time but i can't give you any personalities that that led that effort yes sir in the merchant marine during the sailing ship ending they used to uh inflict the the error of the disagreement immediately the first mate was a tougher sky on the ship and if you gave many lippie come back with no teeth that's pretty effective punishment in addition to that they had the punishment with their keelhaul they put a line under the vessel i i've i've heard that and i was looking forward to finding some examples of keelhauling somewhere in the archives and i never did i can't give you any examples of keelhauling in the united states navy but again there were abuses of flogging i'm sure there were abuses of other other disciplines yes yes sir can you uh tell us something about the decision was made to close the prison how did that come about well the interesting stuff about that yeah i see that this always happens to me my period of expertise is up to 1920 and then everybody wants to know about what happened at the prison since them and i'm not as schooled on that and it's been more embarrassing because i was at the shipyard as a junior officer in 1973 when it closed but i can just remember the directive coming down cost was involved and they they had had a a dip in the prisoner population again so i think it was they they could accommodate the needs that they had for cells as at something far less than the elaborate prison that they had at the time about the best i can do yes when a guy was flogged and it was finished was he left the heel on his own or was he actually treated oh no that's they he was treated by his friends uh he wasn't left there to die by no stretch the imagination and they'd put brine on his wounds or something but it uh uh yeah he was he was treated as best they could but how how effectively can you treat a guy if you're on the asiatic station somewhere and and somebody beats you with a whip you know there's there's not much they can do for you any other questions well thank you very much for your attention