arXiv · 2607.03630
On the inverses of permutation polynomials of the form $h(ψ(x))φ(x)+g(ψ(x))$ over finite fields
Abstract
In this paper, we investigate the compositional inverses of permutation polynomials of the form \[ F(x)=h(ψ(x))φ(x)+g(ψ(x)) \in \mathbb{F}_{q^n}[x], \] where \(ψ(x),φ(x) \in \mathbb{F}_{q^n}[x]\) are additive polynomials, \(h(x), g(x) \in \mathbb{F}_{q^n}[x]\) satisfy $ h(ψ(\mathbb{F}_{q^n})) \subseteq \mathbb{F}_q^*, $ and there exists a polynomial \(\barψ(x) \in \mathbb{F}_{q^n}[x]\) such that $ \barψ(F(x)) = ψ(x). $
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Danyao Wu, Pingzhi Yuan, Xuan Pang. 2026-07-03. On the inverses of permutation polynomials of the form $h(ψ(x))φ(x)+g(ψ(x))$ over finite fields. https://arxiv.org/abs/2607.03630
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