Permutation trinomials over finite fields with even characteristic

TL;DR

This paper introduces new classes of permutation trinomials over finite fields with even characteristic, expanding the limited known examples and contributing to the theoretical understanding of permutation polynomials.

Contribution

It presents novel permutation trinomial constructions over finite fields with even characteristic, broadening the existing catalog of such polynomials.

Findings

New permutation trinomial classes over finite fields with even characteristic

Enhanced understanding of permutation polynomial structures

Potential applications in cryptography and coding theory

Abstract

Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature so far. In this paper we present a number of permutation trinomials over finite fields, which are of different forms.