A recurrent construction of irreducible polynomials of fixed degree over finite fields
Abstract
In this paper we consider in detail the composition of an irreducible polynomial with X2 and suggest a recurrent construction of irreducible polynomials of fixed degree over finite fields of odd characteristics. More precisely, given an irreducible polynomial of degree n and order 2rt with t odd, the construction produces ordt(2)/d irreducible polynomials of degree n and order t for a certain divisor d of n. The construction can be used, for example, to search irreducible polynomials with specific requirements on its coefficients.
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