偶特征有限域上的一些置换五反常项

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-10-23 DOI:10.1016/j.ffa.2025.102742

Farhana Kousar , Maosheng Xiong

引用次数: 0

摘要

在最近的一篇论文[30]中，Zhang等人构造了17个形式为xt+xr1(q−1)+t+xr2(q−1)+t+xr3(q−1)+t+xr4(q−1)+t / Fq2的置换五反常族，其中q=2m。在这篇论文中，我们对这17个家族中的14个提供了一个简单的解释，为什么它们是排列。我们还将这14个科扩展到Fq2上的3类置换五反常。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some permutation pentanomials over finite fields of even characteristic

In a recent paper [30] Zhang et al. constructed 17 families of permutation pentanomials of the form

x^{t} + x^{r_{1} (q - 1) + t} + x^{r_{2} (q - 1) + t} + x^{r_{3} (q - 1) + t} + x^{r_{4} (q - 1) + t}

over

F_{q^{2}}

where

q = 2^{m}

. In this paper for 14 of these 17 families we provide a simple explanation as to why they are permutations. We also extend these 14 families into three general classes of permutation pentanomials over

F_{q^{2}}

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.