置换多项式多元技术的进一步研究

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-06-16 DOI:10.1016/j.ffa.2025.102678

Mu Yuan, Kangquan Li, Longjiang Qu

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引用次数: 0

摘要

排列多项式因其在各个领域的广泛应用而成为研究的热点。基于多元技术，通过三种不同的方法，给出了有限域上具有偶特征的六类置换三项式。第一种方法是所谓的l方法的一种变体。同时，本文的结果推广了前人的一些结果。第二种方法利用这些多项式与Dickson多项式和对称多项式的联系。第三种是基于一个众所周知的引理和有限域的乘法子群上的一些算法。最后，我们证明了所有的排列多项式与已知的排列多项式是qm不等价的。

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Further study on multivariate technique for permutation polynomials

The research of permutation polynomials has been a hot topic due to their wide applications in various areas. Based on the multivariate technique, this paper proposes six classes of permutation trinomials over finite fields with even characteristics via three different approaches. The first approach is a variant of the so-called

L

-method. Meanwhile, the presented results generalize some previous results. The second one employs the connections of these polynomials with Dickson polynomials and symmetric polynomials. The third one is based on a well-known lemma and some arithmetics over the multiplicative subgroup of the finite fields. Ultimately, we show that all presented permutation polynomials are QM-inequivalent to the known ones.

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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.