Some classes of complete permutation polynomials over $\mathbb{F}_q $

Abstract

By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over \(\mathbb{F}_{p^{4k} } \), where \(d = \frac{{p^{4k} - 1}} {{p^k - 1}} + 1\) and \(a \in \mathbb{F}_{p^{4k} }^* \). Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.