New classes of permutation trinomials of F22m

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-03-26 DOI:10.1016/j.ffa.2024.102414

Akshay Ankush Yadav , Indivar Gupta , Harshdeep Singh , Arvind Yadav

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引用次数: 0

Abstract

In recent years, there have been a lot of research towards finding conditions under which the trinomial $x^{r} (x^{α (q - 1)} + x^{β (q - 1)} + 1)$ permutes $F_{2^{2 m}}$ with $α > β$ and r being positive integers. The authors of [6], [10], [24] have determined these conditions when $α \leq 5$ for certain values of β and r. In this paper, we work for $α = 6$ and determine four new classes of such permutation trinomials. Our contribution encompasses the investigation of these unexplored classes. Additionally, we analyze their quasi-multiplicative equivalence with already known permutation trinomials for $m \geq 1$ . Through our research, we demonstrate that two of these determined classes are new, and for others, we explicitly compute the exponent for which they become equivalent.

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F22m 的新类置换三项式

近年来，人们一直在寻找三项式 xr(xα(q-1)+xβ(q-1)+1) 包络 F22m 且 α>β 和 r 为正整数的条件。在本文中，我们研究了 α=6 的情况，并确定了四类新的此类置换三项式。我们的贡献包括对这些未探索类别的研究。此外，我们还分析了它们与已知的 m≥1 的置换三项式的准乘法等价性。通过研究，我们证明了这些确定的类别中有两个是新的，对于其他类别，我们明确计算了它们等价的指数。

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.