A Recurrent Method for Constructing Irreducible Polynomials over Finite Fields

摘要

In this paper we consider irreducibility of the polynomial composition of the form (x~p - x + δ_2)~n P (x~p - x + δ_1/x~p - x + δ_2) over F_q under certain conditions. Furthermore, a computationally simple and explicit method of constructing recursive sequences of irreducible polynomials of degree np~k (k = 1,2, 3, ···) over F_q is given.