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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80643A 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.22 pages, 6 tables, 0 figuresChaotic DynamicsGeneral MathematicsAn 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 sequencestext