Inverses of six classes of permutation polynomials of the form $x+\gamma\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields of even characteristic

TL;DR

This paper determines the compositional inverses of six classes of permutation polynomials over finite fields of even characteristic, specifically those of the form involving trace functions.

Contribution

It provides explicit inverse formulas for six classes of permutation polynomials of a specific form over finite fields of characteristic two.

Findings

Explicit inverses for six classes of permutation polynomials.

Extension of previous work by Jiang et al. on permutation polynomials.

Abstract

Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x+\gamma\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields $\mathbb{F}_{q^2},q=2^n$. In this paper, we find the compositional inverse of six classes of permutation polynomials of this form.