A note on a class of permutation trinomials

Abstract

Let [Formula: see text] denote the finite field with [Formula: see text] elements. In this paper, we investigate the trinomial [Formula: see text] over the finite field [Formula: see text], where [Formula: see text] with [Formula: see text] being a positive integer. We prove that the trinomial [Formula: see text] permutes [Formula: see text] if and only if [Formula: see text] and [Formula: see text] is even. This work is a continuation of the previous work of Bai and Xia [A new class of permutation trinomials constructed from Niho exponents, Cryptogr. Commun. 10 (2018) 1023–1036].