 Using the companion matrix of the characteristic polynomial of the LFSR and denoting the seed as a column vector formula_3, the state of the register in Fibonacci configuration after formula_4 steps is given by

For the Galois form, we have

These forms generalize naturally to arbitrary fields.The following table lists maximal-length polynomials for shift-register lengths up to 24.Note that more than one maximal-length polynomial may exist for any given shift-register length.