Permutation polynomials over finite fields by the local criterion

Danyao Wu; Pingzhi Yuan

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arXiv · 2409.18758

Permutation polynomials over finite fields by the local criterion

Danyao Wu·Pingzhi Yuan

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Abstract

In this paper, we further investigate the local criterion and present a class of permutation polynomials and their compositional inverses over $ \mathbb{F}_{q^2}$. Additionally, we demonstrate that linearized polynomial over $\mathbb{F}_{q^n}$ is a local permutation polynomial with respect to all linear transformations from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q ,$ and that every permutation polynomial is a local permutation polynomial with respect to certain mappings.

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Danyao Wu, Pingzhi Yuan. 2024-09-27. Permutation polynomials over finite fields by the local criterion. https://arxiv.org/abs/2409.18758

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