Irreducible factorization of translates of reversed Dickson polynomials\n over finite fields

2018/02/05 by Ronald M. Evans, Mark Van Veen, Evans, Ron +1
Computer Science · #11T06 #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1802.01739

openalex publication_date 2018/02/05 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

Let F be a field of q elements, where q is a power of an odd prime. Fix\nn = (q+1)/2. For each s \∈ F, we describe all the irreducible factors over\nF of the polynomial g_s(y): = yⁿ + (1-y)ⁿ -s, and we give a necessary and\nsufficient condition on s for g_s(y) to be irreducible.\n

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