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2005•arXiv (Cornell University)Open access

Generating matrices of highest order over a finite field

Piyasi Choudhury

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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.

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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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Available 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.

Key concepts: Finite field, Coding theory, Primitive polynomial, Mathematics, Cryptography, Order (exchange), Matrix (chemical analysis), Field (mathematics)

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