New curves of Kummer type with many rational points over finite fields

IF 1.3 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-12-16 DOI:10.1016/j.ffa.2025.102780

H. Navarro, Luz A. Pérez

引用次数: 0

Abstract

In this paper, we present two methods for constructing curves of Kummer type with many rational points over finite fields. The first method is based on binomials, while the second employs reciprocal polynomials. The latter is an extension of the method introduced by Gupta et al. (2023) [19] over quadratic finite fields, to non-prime finite fields. As a result, we found 63 new records and 37 new entries for the online table of curves with many points found at manYPoints.

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有限域上具有多有理点的Kummer型新曲线

本文给出了在有限域上构造具有多有理点的Kummer型曲线的两种方法。第一种方法是基于二项式，而第二种方法是使用互反多项式。后者是将Gupta等人（2023）[19]在二次有限域上引入的方法推广到非素数有限域。结果，我们发现了63条新记录和37个新条目，用于在线曲线表，其中在manYPoints上发现了许多点。

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.