Some permutation polynomials via linear translators

TL;DR

This paper extends the concept of linear translators in finite fields to construct new classes of permutation polynomials, contributing to the explicit construction methods in number theory.

Contribution

It introduces an extended notion of linear translators and uses it to develop new permutation polynomials over finite fields.

Findings

New classes of permutation polynomials constructed

Extended the concept of linear translators

Provided explicit construction methods

Abstract

Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many scholars constructed some classes of permutation polynomials. Motivated by previous works, we first naturally extend the notion of linear translators and then construct some permutation polynomials.