The study on three classes of permutation quadrinomials over finite fields of odd characteristic

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-04-10 DOI:10.1016/j.ffa.2025.102626

Changhui Chen , Haibin Kan , Jie Peng , Hengtai Wang , Lijing Zheng

引用次数: 0

Abstract

Let p be an odd prime and n a positive integer. This paper focuses on the investigation of permutation quadrinomials with generalized Niho exponents over finite fields of odd characteristic. Inspired by the works in [10], we study two classes of permutation quadrinomials over

F_{p^{n}}

and a class of permutation quadrinomials over

F_{5^{n}}

. Finally, we verify that permutation quadrinomials presented in this paper are multiplicative inequivalent to known ones.

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奇特征有限域上三类置换四项的研究

设p为奇素数，n为正整数。研究了奇特征有限域上具有广义Niho指数的置换四项。受[10]工作的启发，我们研究了Fpn上的两类置换二项式和F5n上的一类置换二项式。最后，我们证明了本文所提出的置换四项与已知的置换四项是乘法不等式。

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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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.