局部最大可恢复编码和 LMR-LCD 编码

IF 1.4 2区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Rajendra Prasad Rajpurohit, Maheshanand Bhaintwal, Charul Rajput
{"title":"局部最大可恢复编码和 LMR-LCD 编码","authors":"Rajendra Prasad Rajpurohit, Maheshanand Bhaintwal, Charul Rajput","doi":"10.1007/s10623-024-01419-5","DOIUrl":null,"url":null,"abstract":"<p>In this work, we propose two new types of codes with locality, namely, locally maximal recoverable (LMR) codes and <span>\\(\\lambda \\)</span>-maximally recoverable (<span>\\(\\lambda \\)</span>-MR) codes. The LMR codes are a subclass of codes with <span>\\((r, \\delta )\\)</span>-locality such that they can correct <i>h</i> additional erasures in any one local set, in addition to having <span>\\((r, \\delta )\\)</span>-locality. These codes are a restricted case of maximally recoverable (MR) codes, which enable recovery from all information-theoretically correctable erasure patterns in a local set. The <span>\\(\\lambda \\)</span>-MR codes are a subclass of LMR codes which can also handle <span>\\(\\lambda \\)</span> erasures from any coordinate positions. We give constructions for both of these families of codes. We also study the LMR codes that satisfy the complementary dual property. It is well known that codes with this property are capable of safeguarding communication systems against fault injection attacks. We give a construction of distance-optimal cyclic LMR codes that satisfy the complementary dual property.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"159 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Locally maximal recoverable codes and LMR-LCD codes\",\"authors\":\"Rajendra Prasad Rajpurohit, Maheshanand Bhaintwal, Charul Rajput\",\"doi\":\"10.1007/s10623-024-01419-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work, we propose two new types of codes with locality, namely, locally maximal recoverable (LMR) codes and <span>\\\\(\\\\lambda \\\\)</span>-maximally recoverable (<span>\\\\(\\\\lambda \\\\)</span>-MR) codes. The LMR codes are a subclass of codes with <span>\\\\((r, \\\\delta )\\\\)</span>-locality such that they can correct <i>h</i> additional erasures in any one local set, in addition to having <span>\\\\((r, \\\\delta )\\\\)</span>-locality. These codes are a restricted case of maximally recoverable (MR) codes, which enable recovery from all information-theoretically correctable erasure patterns in a local set. The <span>\\\\(\\\\lambda \\\\)</span>-MR codes are a subclass of LMR codes which can also handle <span>\\\\(\\\\lambda \\\\)</span> erasures from any coordinate positions. We give constructions for both of these families of codes. We also study the LMR codes that satisfy the complementary dual property. It is well known that codes with this property are capable of safeguarding communication systems against fault injection attacks. We give a construction of distance-optimal cyclic LMR codes that satisfy the complementary dual property.</p>\",\"PeriodicalId\":11130,\"journal\":{\"name\":\"Designs, Codes and Cryptography\",\"volume\":\"159 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Designs, Codes and Cryptography\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10623-024-01419-5\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Designs, Codes and Cryptography","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10623-024-01419-5","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0

摘要

在这项工作中,我们提出了两种具有局部性的新型编码,即局部最大可恢复(LMR)编码和最大可恢复(MR)编码。LMR码是具有((r, \delta))局部性的码的一个子类,它们除了具有((r, \delta))局部性之外,还能在任意一个局部集中纠正h个额外的擦除。这些编码是最大可恢复(MR)编码的一种受限情况,最大可恢复编码可以从局部集合中的所有信息理论上可纠正的擦除模式中恢复。(\λ\)-MR码是LMR码的一个子类,它也可以处理来自任何坐标位置的(\λ\)擦除。我们给出了这两类编码的构造。我们还研究了满足互补对偶属性的 LMR 码。众所周知,具有这一特性的编码能够保护通信系统免受故障注入攻击。我们给出了满足互补对偶性的距离最优循环 LMR 码的构造。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Locally maximal recoverable codes and LMR-LCD codes

Locally maximal recoverable codes and LMR-LCD codes

In this work, we propose two new types of codes with locality, namely, locally maximal recoverable (LMR) codes and \(\lambda \)-maximally recoverable (\(\lambda \)-MR) codes. The LMR codes are a subclass of codes with \((r, \delta )\)-locality such that they can correct h additional erasures in any one local set, in addition to having \((r, \delta )\)-locality. These codes are a restricted case of maximally recoverable (MR) codes, which enable recovery from all information-theoretically correctable erasure patterns in a local set. The \(\lambda \)-MR codes are a subclass of LMR codes which can also handle \(\lambda \) erasures from any coordinate positions. We give constructions for both of these families of codes. We also study the LMR codes that satisfy the complementary dual property. It is well known that codes with this property are capable of safeguarding communication systems against fault injection attacks. We give a construction of distance-optimal cyclic LMR codes that satisfy the complementary dual property.

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
Designs, Codes and Cryptography
Designs, Codes and Cryptography 工程技术-计算机:理论方法
CiteScore
2.80
自引率
12.50%
发文量
157
审稿时长
16.5 months
期刊介绍: Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.
×
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