Constructing permutations of finite fields via linear translators

TL;DR

This paper introduces new methods for constructing permutation polynomials over finite fields using functions with linear translators, expanding the toolkit for finite field permutations.

Contribution

It presents novel families of permutation polynomials derived from functions with linear translators, offering new constructions in finite field theory.

Findings

Several new families of permutation polynomials are constructed.

The methods leverage functions with linear translators for permutation generation.

The results expand the known classes of permutation polynomials.

Abstract

We describe several families of permutation polynomials obtained using functions with linear translators.