The compositional inverses of permutation polynomials of the form $\sum_{i=1}^kb_i(x^{p^m}+x+\delta)^{s_i}-x$ over $\mathbb{F}_{p^{2m}}$

Danyao Wu; Pingzhi Yuan; Huanhuan Guan; Juan Li

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arXiv · 2409.18662

The compositional inverses of permutation polynomials of the form $\sum_{i=1}^kb_i(x^{p^m}+x+\delta)^{s_i}-x$ over $\mathbb{F}_{p^{2m}}$

Danyao Wu·Pingzhi Yuan·Huanhuan Guan·Juan Li

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Abstract

In this paper, we present the compositional inverses of several classes permutation polynomials of the form $\sum_{i=1}^kb_i(x^{p^m}+x+\delta)^{s_i}-x$ over $\mathbb{F}_{p^{2m}}$, where for $1\leq i \leq k,$ $s_i, m$ are positive integers, $b_i, \delta \in \mathbb{F}_{p^{2m}},$ and $p$ is prime.

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Danyao Wu, Pingzhi Yuan, Huanhuan Guan, Juan Li. 2024-09-27. The compositional inverses of permutation polynomials of the form $\sum_{i=1}^kb_i(x^{p^m}+x+\delta)^{s_i}-x$ over $\mathbb{F}_{p^{2m}}$. https://arxiv.org/abs/2409.18662

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