两类线性码的完全权值枚举数和权值层次

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-03 DOI:10.1016/j.disc.2025.114510

Jiawei He, Yinjin Liao

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引用次数: 0

摘要

线性编码的广义汉明权值的研究是编码理论研究的一个重要领域，因为它提供了有价值的编码结构信息，在各种应用中对决定编码的性能起着至关重要的作用。本文通过选择两个特定的定义集，设计了两类不同的线性码。首先，确定了这些规范的权重分布。随后，通过详细分析定义集与所有r维子空间的对偶之间的交点，成功地确定了两类线性码的完全权层次。

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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Complete weight enumerators and weight hierarchies of two classes of linear codes

The study of generalized Hamming weights for linear coding is an important area of research in coding theory as it provides valuable structural information about coding and plays a crucial role in determining the performance of coding in various applications. In this paper, two distinct classes of linear codes are devised through the selection of two particular defining sets. Initially, the weight distributions of these codes are ascertained. Subsequently, by conducting a detailed analysis of the intersections between the defining sets and the duals of all r-dimensional subspaces, the complete weight hierarchies of the two classes of linear codes are successfully determined.

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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.