A Search of all of the irreducible polynomials of degree m over GF(2)

Abstract

A fast method for finding irreducible polynomial of degree m over GF(2) is proposed in this paper. Given an arbitrary irreducible polynomial of degree m and any proper primitive element, the finite field GF(2m) is generated. From this finite field, one can generate all the irreducible polynomials over GF (2) with degree less than or equal to m. These irreducible polynomials are useful in constructing finite fields for applications in error correcting code, cryptography and other related subjects.