Generating matrices of highest order over a finite field

Details Generating matrices of highest order over a finite field Generating matrices of highest order over a finite field

2005-11-27

arxiv.org/abs/math/0511651v1

Mathematics

Group Theory

Scientific paper

Shift registers/Primitive polynomials find applications in various branches of Mathematics, Coding Theory and Cryptography. Matrix analogues of primitive polynomials do exist. In this paper, an algorithmic approach to generating all such matrices over GF(2) has been presented. A technique for counting all such n x n matrices over GF(2) is also presented. The technique may be easily extended to other finite fields.

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