Several classes of wide minimal binary linear codes based on general Maiorana-McFarland class

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-18 DOI:10.1016/j.disc.2025.114642

Xiaoni Du , Siqi Gao , Wenping Yuan , Xingbin Qiao

引用次数: 0

Abstract

Minimal linear codes have important applications in secret sharing schemes and secure two-party computation. In this paper, we extend the construction of wide minimal binary linear codes presented by Ding et al. [8] (2018) to a more general case. More specifically, we first construct a class of Boolean functions belonging to the general Maiorana-McFarland class with more flexible parameters. Then we provide a framework for examining the Walsh transform of the new functions via the Krawtchouk polynomial. Finally, we obtain several classes of wide minimal binary linear codes with a few weights and determine their weight distribution explicitly. Our results cover all the related existing ones.

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基于一般Maiorana-McFarland类的几类宽最小二进制线性码

最小线性码在秘密共享方案和安全的双方计算中有着重要的应用。在本文中，我们将Ding等人[8]（2018）提出的宽最小二进制线性码的构造扩展到更一般的情况。更具体地说，我们首先构造了一类布尔函数，该类属于一般的Maiorana-McFarland类，具有更灵活的参数。然后，我们提供了一个框架，通过克劳楚克多项式来检验新函数的沃尔什变换。最后，我们得到了几类具有少量权值的宽最小二进制线性码，并明确地确定了它们的权值分布。我们的结果涵盖了所有相关的现有结果。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.