On a Class of Permutation Rational Functions Involving Trace Maps

TL;DR

This paper investigates a specific class of permutation rational functions over finite fields, constructed via trace maps, focusing on quadratic and cubic extensions, and analyzes their properties through polynomial irreducibility.

Contribution

It introduces a new class of permutation rational functions involving trace maps and provides criteria for their permutation behavior over finite field extensions.

Findings

Characterization of permutation rational functions using trace maps

Conditions for absolute irreducibility of related polynomials

Insights into permutation properties over quadratic and cubic extensions

Abstract

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on extensions of finite fields, especially for the cases of quadratic and cubic extensions. Our achievements are obtained by investigating absolute irreducibility of some polynomials in two indeterminates.