Covering Codes for the Fixed Length Levenshtein Metric

IF 0.5 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS
{"title":"Covering Codes for the Fixed Length Levenshtein Metric","authors":"","doi":"10.1134/s0032946023020023","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>A covering code, or a covering, is a set of codewords such that the union of balls centered at these codewords covers the entire space. As a rule, the problem consists in finding the minimum cardinality of a covering code. For the classical Hamming metric, the size of the smallest covering code of a fixed radius <span> <span>\\(R\\)</span> </span> is known up to a constant factor. A similar result has recently been obtained for codes with <span> <span>\\(R\\)</span> </span> insertions and for codes with <span> <span>\\(R\\)</span> </span> deletions. In the present paper we study coverings of a space for the fixed length Levenshtein metric, i.e., for <span> <span>\\(R\\)</span> </span> insertions and <span> <span>\\(R\\)</span> </span> deletions. For <span> <span>\\(R=1\\)</span> </span> and <span> <span>\\(2\\)</span> </span>, we prove new lower and upper bounds on the minimum cardinality of a covering code, which differ by a constant factor only.</p>","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Problems of Information Transmission","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s0032946023020023","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0

Abstract

A covering code, or a covering, is a set of codewords such that the union of balls centered at these codewords covers the entire space. As a rule, the problem consists in finding the minimum cardinality of a covering code. For the classical Hamming metric, the size of the smallest covering code of a fixed radius \(R\) is known up to a constant factor. A similar result has recently been obtained for codes with \(R\) insertions and for codes with \(R\) deletions. In the present paper we study coverings of a space for the fixed length Levenshtein metric, i.e., for \(R\) insertions and \(R\) deletions. For \(R=1\) and \(2\) , we prove new lower and upper bounds on the minimum cardinality of a covering code, which differ by a constant factor only.

固定长度列文士坦度量的覆盖编码
摘要 覆盖编码或称覆盖,是一组编码,使得以这些编码为中心的球的联合覆盖整个空间。通常,问题在于找到覆盖码的最小心率。对于经典的汉明度量,已知固定半径 \(R\)的最小覆盖码的大小为一个常数。最近,对于插入(R)的编码和删除(R)的编码也得到了类似的结果。在本文中,我们研究了固定长度莱文斯坦度量空间的覆盖,即针对插入和删除的覆盖。对于 \(R=1\) 和 \(2\) ,我们证明了覆盖代码最小心数的新的下界和上界,它们只相差一个常数因子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Problems of Information Transmission
Problems of Information Transmission 工程技术-计算机:理论方法
CiteScore
2.00
自引率
25.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: Problems of Information Transmission is of interest to researcher in all fields concerned with the research and development of communication systems. This quarterly journal features coverage of statistical information theory; coding theory and techniques; noisy channels; error detection and correction; signal detection, extraction, and analysis; analysis of communication networks; optimal processing and routing; the theory of random processes; and bionics.
×
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