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arXiv · 2607.03638

The compositional inverses of the permutation polynomials of the form $x+\gamma\operatorname{Tr}_{q}^{q^n}(H(x))$ over $\mathbb{F}_{q^n}$

Danyao Wu·Xuan Pang·Zilong He·Pingzhi Yuan
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Abstract

This paper focuses on computing the compositional inverses of permutation polynomials of the form $x+\gamma \operatorname{Tr}_{q}^{q^{n}}(H(x))$ over finite fields via the local method. We explicitly construct compositional inverses for four families of permutation polynomials of this type over $\mathbb{F}_{q^2}$, another four families over $\mathbb{F}_{q^3}$, and one general family over $\mathbb{F}_{q^n}$. The closed-form inverse expressions derived in this work supplement the theory of trace permutation polynomials.

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Danyao Wu, Xuan Pang, Zilong He, Pingzhi Yuan. 2026-07-03. The compositional inverses of the permutation polynomials of the form $x+\gamma\operatorname{Tr}_{q}^{q^n}(H(x))$ over $\mathbb{F}_{q^n}$. https://arxiv.org/abs/2607.03638

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