New Classes of Permutation Binomials and Permutation Trinomials over Finite Fields

TL;DR

This paper introduces new classes of permutation binomials and trinomials over finite fields, expanding the known families and highlighting their potential applications in various scientific and engineering domains.

Contribution

The paper constructs several new classes of permutation binomials and trinomials, some generalizing previously known permutation polynomials over finite fields.

Findings

New permutation binomials and trinomials are constructed.

Some classes generalize known permutation polynomials.

Results have implications for coding theory and cryptography.

Abstract

Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication theory and so on. Permutation binomials and trinomials attract people's interest due to their simple algebraic form and additional extraordinary properties. In this paper, several new classes of permutation binomials and permutation trinomials are constructed. Some of these permutation polynomials are generalizations of known ones.