Algebraic Structure of Permutational Polynomials over $\mathbb{F}_{q^n}$

TL;DR

This paper introduces a novel algebraic framework for permutation polynomials over finite fields, leading to new classes of such polynomials and resolving an open problem in the field.

Contribution

It presents a new algebraic structure for permutation polynomials over finite fields and applies it to generate new classes and solve an open problem.

Findings

New algebraic structure for permutation polynomials

Construction of new permutation polynomial classes

Resolution of an open problem in the literature

Abstract

In this paper, we propose a new algebraic structure of permutation polynomials over $\mathbb{F}_{q^n}$. As an application of this new algebraic structure, we give some classes of new PPs over $\mathbb{F}_{q^n}$ and answer an open problem in Charpin and Kyureghyan.