\({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3} \)上的一些代码及其在秘密共享方案中的应用

IF 0.9 Q2 MATHEMATICS
Karima Chatouh
{"title":"\\({\\mathcal {R}}={\\mathcal {R}}_{1}{\\mathcal {R}}_{2}{\\mathcal {R}}_{3} \\)上的一些代码及其在秘密共享方案中的应用","authors":"Karima Chatouh","doi":"10.1007/s13370-023-01143-8","DOIUrl":null,"url":null,"abstract":"<div><p>Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring <span>\\({\\mathcal {R}}={\\mathcal {R}}_{1}{\\mathcal {R}}_{2}{\\mathcal {R}}_{3}\\)</span>. We have introduced a novel family of linear codes over <span>\\({\\mathbb {F}}_{p}\\)</span>. These codes have been extensively examined with respect to their properties, such as code minimality, weight distribution, and their applications in secret sharing schemes. In addition to this investigation, we have discovered that these codes are also applicable to the association schemes of linear torsion codes for simplex and MacDonald codes over. <span>\\({\\mathcal {R}}={\\mathcal {R}}_{1}{\\mathcal {R}}_{2}{\\mathcal {R}}_{3}\\)</span>.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some codes over \\\\({\\\\mathcal {R}}={\\\\mathcal {R}}_{1}{\\\\mathcal {R}}_{2}{\\\\mathcal {R}}_{3} \\\\) and their applications in secret sharing schemes\",\"authors\":\"Karima Chatouh\",\"doi\":\"10.1007/s13370-023-01143-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring <span>\\\\({\\\\mathcal {R}}={\\\\mathcal {R}}_{1}{\\\\mathcal {R}}_{2}{\\\\mathcal {R}}_{3}\\\\)</span>. We have introduced a novel family of linear codes over <span>\\\\({\\\\mathbb {F}}_{p}\\\\)</span>. These codes have been extensively examined with respect to their properties, such as code minimality, weight distribution, and their applications in secret sharing schemes. In addition to this investigation, we have discovered that these codes are also applicable to the association schemes of linear torsion codes for simplex and MacDonald codes over. <span>\\\\({\\\\mathcal {R}}={\\\\mathcal {R}}_{1}{\\\\mathcal {R}}_{2}{\\\\mathcal {R}}_{3}\\\\)</span>.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-11-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-023-01143-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-023-01143-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

自编码理论诞生以来,单纯形码和麦克唐纳码一直受到研究者的极大关注。在这项工作中,我们提出了单纯形和麦克唐纳码在环\({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3}\)上的线性扭转码的构造。我们在\({\mathbb {F}}_{p}\)上介绍了一个新的线性码族。对这些代码的性质进行了广泛的研究,例如代码最小化、权重分布以及它们在秘密共享方案中的应用。除此之外,我们还发现这些码也适用于单纯形和麦克唐纳码的线性扭转码的关联方案。\({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3}\)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Some codes over \({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3} \) and their applications in secret sharing schemes

Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring \({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3}\). We have introduced a novel family of linear codes over \({\mathbb {F}}_{p}\). These codes have been extensively examined with respect to their properties, such as code minimality, weight distribution, and their applications in secret sharing schemes. In addition to this investigation, we have discovered that these codes are also applicable to the association schemes of linear torsion codes for simplex and MacDonald codes over. \({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3}\).

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Afrika Matematika
Afrika Matematika MATHEMATICS-
CiteScore
2.00
自引率
9.10%
发文量
96
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信