More Classes of Complete Permutation Polynomials over $\F_q$

TL;DR

This paper introduces new classes of complete permutation polynomials and multinomials over finite fields, expanding the known families using Zieve's criterion and generalizing recent results.

Contribution

It provides several new classes of complete permutation monomials and a generalized class of permutation multinomials over finite fields.

Findings

New classes of complete permutation monomials over _{q^r}

A generalized class of complete permutation multinomials

Enhanced understanding of permutation polynomial structures

Abstract

In this paper, by using a powerful criterion for permutation polynomials given by Zieve, we give several classes of complete permutation monomials over $\F_{q^r}$. In addition, we present a class of complete permutation multinomials, which is a generalization of recent work.