On permutation quadrinomials from Niho exponents in characteristic two

IF 1.2 3区数学 Q1 MATHEMATICS Finite Fields and Their Applications Pub Date : 2024-03-26 DOI:10.1016/j.ffa.2024.102418

Vincenzo Pallozzi Lavorante

引用次数: 0

Abstract

Recently Zheng et al. [18] characterized the coefficients of $f (x) = x + a_{1} x^{s_{1} (2^{m} - 1) + 1} + a_{2} x^{s_{2} (2^{m} - 1) + 1} + a_{3} x^{s_{3} (2^{m} - 1) + 1}$ over $F_{2^{2 m}}$ that lead $f (x)$ to be a permutation of $F_{2^{2 m}}$ for $(s_{1}, s_{2}, s_{3}) = (\frac{1}{4}, 1, \frac{3}{4})$ . They left open the question whether those conditions were also necessary. In this paper, we give a positive answer to that question, solving their conjecture.

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从特征二中的尼霍指数论 permutation quadrinomials from Niho exponents

最近，Zheng 等人[18]描述了 F22m 上 f(x)=x+a1xs1(2m-1)+1+a2xs2(2m-1)+1+a3xs3(2m-1)+1 的系数，这些系数导致 f(x) 在 (s1,s2,s3)=(14,1,34) 时成为 F22m 的置换。至于这些条件是否也是必要条件，他们还没有回答。在本文中，我们给出了肯定的答案，解决了他们的猜想。

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.

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