A New Method of Construction of Permutation Trinomials with Coefficients 1

TL;DR

This paper introduces a novel method for constructing permutation trinomials with coefficients 1 over finite fields, expanding the toolkit for researchers and providing explicit inverses in specific cases.

Contribution

It presents a new construction technique for permutation trinomials with coefficient 1, based on reversing Tu's method, and derives explicit inverses for certain classes.

Findings

New construction method for permutation trinomials

Explicit inverses for a class of permutation trinomials

Enhanced understanding of permutation polynomial structures

Abstract

Permutation polynomials over finite fields are an interesting and constantly active research subject of study for many years. They have important applications in areas of mathematics and engineering. In recent years, permutation binomials and permutation trinomials attract people's interests due to their simple algebraic forms. In this paper, by reversely using Tu's method for the characterization of permutation polynomials with exponents of Niho type, we propose a new method to construct permutation trinomials with coefficients 1. Moreover, we give the explicit compositional inverses of a class of permutation trinomials for a special case.