On the inverses of permutation polynomials of the form $h(\psi(x))\varphi(x)+g(\psi(x))$ over finite fields

Danyao Wu; Pingzhi Yuan; Xuan Pang

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arXiv · 2607.03630

On the inverses of permutation polynomials of the form $h(\psi(x))\varphi(x)+g(\psi(x))$ over finite fields

Danyao Wu·Pingzhi Yuan·Xuan Pang

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Abstract

In this paper, we investigate the compositional inverses of permutation polynomials of the form \[ F(x)=h(\psi(x))\varphi(x)+g(\psi(x)) \in \mathbb{F}_{q^n}[x], \] where $\psi(x),\varphi(x) \in \mathbb{F}_{q^n}[x]$ are additive polynomials, $h(x), g(x) \in \mathbb{F}_{q^n}[x]$ satisfy $ h(\psi(\mathbb{F}_{q^n})) \subseteq \mathbb{F}_q^*, $ and there exists a polynomial $\bar{\psi}(x) \in \mathbb{F}_{q^n}[x]$ such that $ \bar{\psi}(F(x)) = \psi(x). $

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Danyao Wu, Pingzhi Yuan, Xuan Pang. 2026-07-03. On the inverses of permutation polynomials of the form $h(\psi(x))\varphi(x)+g(\psi(x))$ over finite fields. https://arxiv.org/abs/2607.03630

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