Note on Irreducible Polynomials over Finite Field
DOI:
https://doi.org/10.29020/nybg.ejpam.v14i1.3898Keywords:
Finite fields, Irreducible polynomials, Vi\'ete theorem.Abstract
In this note we extend an irreducibility criterion of polynomial over finite fields. We prove the irreducibility of the polynomial P(Y ) = Y n + 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.
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