形式为 $x+\gamma \mathrm{Tr}(H(x))$ 的置换多项式
数论
2025-07-02 v1
摘要
给定 上的多项式 ，我们研究形式为 过 的置换多项式。设 \]P_H=\{\gamma\in \mathbb{F}_{q^n} : x+\gamma \mathrm{Tr}(H(x))~\text{是置换多项式}\}.\] 我们给出了集合 的一些性质，特别是其与线性翻译器之间的关系。此外，我们获得了集合 基数的一个有效上界，表明该上界可达到 。 Furthermore, we prove that when the cardinality of the set reaches this upper bound, the function must be an -linear function. Finally, we study two classes of functions over and determine the corresponding sets . The sizes of these sets are all relatively small, even only including the trivial case.
引用
@article{arxiv.2507.00781,
title = {Permutation polynomials of the form $x+\gamma \mathrm{Tr}(H(x))$},
author = {Yangcheng Li and Xuan Pang and Pingzhi Yuan and Yuanpeng Zeng},
journal= {arXiv preprint arXiv:2507.00781},
year = {2025}
}