Binary sequence family with both small cross-correlation and large family complexity

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-04-29 DOI:10.1016/j.ffa.2024.102440

Huaning Liu, Xi Liu

引用次数: 0

Abstract

Ahlswede, Khachatrian, Mauduit and Sárközy introduced the notion of family complexity, Gyarmati, Mauduit and Sárközy introduced the cross-correlation measure for families of binary sequences. It is a challenging problem to find families of binary sequences with both small cross-correlation measure and large family complexity. In this paper we present a family of binary sequences with both small cross-correlation measure and large family complexity by using the properties of character sums and primitive normal elements in finite fields.

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交叉相关性小而族复杂性大的二进制序列族

Ahlswede、Khachatrian、Mauduit 和 Sárközy 提出了族复杂度的概念，Gyarmati、Mauduit 和 Sárközy 则提出了二元序列族的交叉相关度量。如何找到既有小的交叉相关度又有大的族复杂度的二进制序列族是一个具有挑战性的问题。在本文中，我们利用有限域中的特征和与基元法元的性质，提出了一个既具有较小的交叉相关度又具有较大的族复杂性的二进制序列族。

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.