New Permutation Reversed Dickson Polynomials over Finite Fields

Abstract

Let [Formula: see text] be an odd prime, and [Formula: see text], [Formula: see text] be nonnegative integers. Let [Formula: see text] be the reversed Dickson polynomial of the [Formula: see text]-th kind. In this paper, by using Hermite's criterion, we study the permutational properties of the reversed Dickson polynomials [Formula: see text] over finite fields in the case of [Formula: see text] with [Formula: see text]. In particular, we provide some precise characterizations for [Formula: see text] being permutation polynomials over finite fields with characteristic [Formula: see text] when [Formula: see text], or [Formula: see text], or [Formula: see text].