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

Abstract

Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x+\gamma {\mathrm{Tr}}_q^{q^2}(h(x))$ 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.