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

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

引用次数: 0

Abstract

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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超简单(v, 5, 2)定向设计及其最小定义集在LDPC码中的应用

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。

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Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

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1.40

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0.00%

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