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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

Ricardo Lopez-Ruiz
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Abstract

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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Ricardo Lopez-Ruiz. 2004-01-10. 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. https://arxiv.org/abs/nlin/0401011

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