An approach to the problem of generating irreducible polynomials over the finite field GF(2) and its relationship with the problem of periodicity on the space of binary sequences

Details An approach to the problem of generating irreducible polynomials over the finite field GF(2) and its relationship with the problem of periodicity on the space of binary sequences An approach to the problem of generating irreducible polynomials over the finite field GF(2) and its relationship with the problem of periodicity on the space of binary sequences

2004-01-10

arxiv.org/abs/nlin/0401011v1

Nonlinear Sciences

Chaotic Dynamics

22 pages, 6 tables, 0 figures

Scientific paper

A method for generating irreducible polynomials of degree n over the finite field GF(2) is proposed. The irreducible polynomials are found by solving a system of equations that brings the information on the internal properties of the splitting field GF(2^n) . Also, the choice of a primitive normal basis allows us to build up a natural representation of GF(2^n) in the space of n-binary sequences. Illustrative examples are given for the lowest orders.

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