超简单(v, 5, 2)定向设计及其最小定义集在LDPC码中的应用

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2023-11-26 DOI:10.1007/s41980-023-00835-y

Maryam Mohammadnezhad, Somayye Golalizadeh, Mahsa Boostan, Nasrin Soltankhah

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引用次数: 0

摘要

在本文中，我们证明了对于所有\(v\equiv 0,1\) (mod 5)和\(v\ge 15\)，存在一个超简单的(v, 5,2)定向设计。此外，对于这些参数，存在一个超简单(v, 5,2)定向设计，使得其最小定义集包含至少一半的块。此外，我们还证明了这些设计对于构造LDPC码的奇偶校验矩阵是有用的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Super-Simple (v, 5, 2) Directed Designs and Their Smallest Defining Sets with Application in LDPC Codes

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Super-Simple (v, 5, 2) Directed Designs and Their Smallest Defining Sets with Application in LDPC Codes

In this paper, we show that for all \(v\equiv 0,1\) (mod 5) and \(v\ge 15\), there exists a super-simple (v, 5, 2) directed design. Moreover, for these parameters, there exists a super-simple (v, 5, 2) directed design such that its smallest defining sets contain at least half of its blocks. Also, we show that these designs are useful in constructing parity-check matrices of LDPC codes.

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来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.