Note on Irreducible Polynomials over Finite Field

Amara Chandoul, Alanod M. Sibih

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.

Keywords

Finite fields, Irreducible polynomials, Vi\'ete theorem.

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