Two Classes of Irreducible Polynomials over Finite Fields

Abstract

Let p be a prime, q be a power of p and t be a positive integer. In this paper, we construct stable polynomials of the form over by Capelli's lemma. We also solve the problem by establishing equivalent conditions for the irreducibility of the trinomial , thereby characterizing its inverse stability over . Moreover, when p is odd and t > s ≥ 0, we prove that the trinomial is not stable over .