A note on the permutation behaviour of the polynomial $g_{n,q}$

TL;DR

This paper introduces a class of permutation polynomials over finite fields of order q^{3k} with q=4, along with a generalization, contributing to the understanding of permutation polynomial behavior.

Contribution

It presents a new class of permutation polynomials over finite fields and extends the results to a broader case, advancing permutation polynomial theory.

Findings

Identified a specific class of permutation polynomials over f_{4^{3k}}.

Provided a generalization of these permutation polynomials.

Enhanced understanding of permutation polynomial structures.

Abstract

Let $q=4$ and $k$ a positive integer. In this short note, we present a class of permutation polynomials over $\Bbb F_{q^{3k}}$. We also present a generalization.