Further Results on Permutation Polynomials over Finite Fields

TL;DR

This paper develops general theorems on permutation polynomials over finite fields and presents new classes of explicit permutation polynomials as applications of these theorems.

Contribution

The paper introduces new general theorems and constructs explicit classes of permutation polynomials over finite fields.

Findings

New theorems on permutation polynomials

Explicit classes of permutation polynomials over finite fields

Demonstrated applications of the theorems

Abstract

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a demonstration of the theorems, we present a number of classes of explicit permutation polynomials on $\gf_q$.