Generating matrices of highest order over a finite field

2005/11/27 by Piyasi Choudhury, Choudhury, Piyasi
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.math/0511651

arxiv created 2005/11/27 · openalex publication_date 2005/11/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• An algorithm for determining the irreducible polynomials over finite fields
• On the number of permutation polynomials over a finite field
• Primitive transformation shift registers of order two over fields of\n characteristic two
• Generating large non-singular matrices over an arbitrary field with blocks of full rank
• Random Generator of Orthogonal Matrices in Finite Fields