Results 1 to 3 of 3  Math Help - Galois fields    1. #1
Junior Member     Feb 2009      Galois fields      Hello
everybody,     i just started studying coding theory from the
book "error control coding" by lin and costello. In the 2nd
chapter he has given a brief overview of the galois fields. No
there are a few confusion that i have and i would be thankful to
whoever can help me calrify them.      1. While defining a field
(or a group) it sometimes seems to me that you can define
addition and multiplication whatever way u want it . like
sometimes its modulo m where m is the size of the finite field
or group sometimes its polynomial addition etc. so please kindly
can somebody explain what are the restriction on how we define
these binary operators.      2. Now it was mentioned in the book
that galois fields (considering modulo addition and modulo
multiplication) exist for size p^k where p is a prime and k is a
positive integer. Why?. i tried to construct for a couple of non
primes but the table for mu