Note on Irreducible Polynomials over Finite Field

Abstract

In this note we extend an irreducibility criterion of polynomial over finite fields. We
prove the irreducibility of the polynomial P(Y ) = Yn + λn−1Y n−1 + λn−2Y n−2 + · · · + λ1Y + λ0, such that λ0 6= 0, deg λn−2 = 2 deg λn−1 + l > deg λi, for all i 6= n − 2 and odd integer l.