Recurrent Methods for Constructing Irreducible Polynomials over GF(2s)

Abstract

The paper is devoted to some results concerning the constructive theory of the synthesis of irreducible polynomials over Galois fields GF(q), q=2s. New methods for the construction of irreducible polynomials of higher degree over GF(q) from a given one are worked out. The complexity of calculations does not exceed O(n3) single operations, where n denotes the degree of the given irreducible polynomial. Furthermore, a recurrent method for constructing irreducible (including self-reciprocal) polynomials over finite fields of even characteristic is proposed.