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
  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. 
Ricardo Lopez-Ruiz