A recurrent construction of irreducible polynomials of fixed degree over finite fields
Gohar Kyureghyan, Melsik K. Kyureghyan · Applicable Algebra in Engineering Communication and Computing · 2020
Abstract In this paper we consider in detail the composition of an irreducible polynomial with $$X^2$$ X 2 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 $$2^rt$$ 2 r t with t odd, the construction produces $$ord_t(2)$$ o r d t ( 2 ) irreducible polynomials of degree n and order t. The construction can be used for example to search irreducible polynomials with specific requirements on its coefficients.