关于一类置换多项式及其倒数

IF 1.2 3区数学 Q1 MATHEMATICS Finite Fields and Their Applications Pub Date : 2024-03-18 DOI:10.1016/j.ffa.2024.102403

Ruikai Chen , Sihem Mesnager

引用次数: 0

摘要

我们介绍了一类 Fqn 上的置换多项式，对于 Fqn 上的某个 q 线性多项式 L，这些多项式可以写成 L(x)xq+1 或 L(xq+1)x。此外，我们还能以更一般的形式推导出更多的置换多项式。

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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On a class of permutation polynomials and their inverses

We introduce a class of permutation polynomial over $F_{q^{n}}$ that can be written in the form $\frac{L (x)}{x^{q + 1}}$ or $\frac{L (x^{q + 1})}{x}$ for some q-linear polynomial L over $F_{q^{n}}$ . Specifically, we present those permutation polynomials explicitly as well as their inverses. In addition, more permutation polynomials can be derived in a more general form.

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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.

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