{"title":"利用同质距离校正重复突发的线性编码","authors":"","doi":"10.1007/s00224-024-10166-y","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>The homogeneous weight (metric) is useful in the construction of codes over a ring of integers <span> <span>\\(\\mathbb {Z}_{p^l}\\)</span> </span> (<em>p</em> prime and <span> <span>\\(l \\ge 1\\)</span> </span> an integer). It becomes Hamming weight when the ring is taken to be a finite field and becomes Lee weight when the ring is taken to be <span> <span>\\(\\mathbb {Z}_{4}\\)</span> </span>. This paper presents homogeneous weight distribution and total homogeneous weight of burst and repeated burst errors in the code space of <em>n</em>-tuples over <span> <span>\\(\\mathbb {Z}_{p^l}\\)</span> </span>. Necessary and sufficient conditions for existence of an (<em>n</em>, <em>k</em>) linear code over <span> <span>\\(\\mathbb {Z}_{p^l}\\)</span> </span> correcting the error patterns with respect to the homogeneous weight are derived.</p>","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear Codes Correcting Repeated Bursts Equipped with Homogeneous Distance\",\"authors\":\"\",\"doi\":\"10.1007/s00224-024-10166-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>The homogeneous weight (metric) is useful in the construction of codes over a ring of integers <span> <span>\\\\(\\\\mathbb {Z}_{p^l}\\\\)</span> </span> (<em>p</em> prime and <span> <span>\\\\(l \\\\ge 1\\\\)</span> </span> an integer). It becomes Hamming weight when the ring is taken to be a finite field and becomes Lee weight when the ring is taken to be <span> <span>\\\\(\\\\mathbb {Z}_{4}\\\\)</span> </span>. This paper presents homogeneous weight distribution and total homogeneous weight of burst and repeated burst errors in the code space of <em>n</em>-tuples over <span> <span>\\\\(\\\\mathbb {Z}_{p^l}\\\\)</span> </span>. Necessary and sufficient conditions for existence of an (<em>n</em>, <em>k</em>) linear code over <span> <span>\\\\(\\\\mathbb {Z}_{p^l}\\\\)</span> </span> correcting the error patterns with respect to the homogeneous weight are derived.</p>\",\"PeriodicalId\":22832,\"journal\":{\"name\":\"Theory of Computing Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Computing Systems\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s00224-024-10166-y\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Computing Systems","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00224-024-10166-y","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}
Linear Codes Correcting Repeated Bursts Equipped with Homogeneous Distance
Abstract
The homogeneous weight (metric) is useful in the construction of codes over a ring of integers \(\mathbb {Z}_{p^l}\) (p prime and \(l \ge 1\) an integer). It becomes Hamming weight when the ring is taken to be a finite field and becomes Lee weight when the ring is taken to be \(\mathbb {Z}_{4}\). This paper presents homogeneous weight distribution and total homogeneous weight of burst and repeated burst errors in the code space of n-tuples over \(\mathbb {Z}_{p^l}\). Necessary and sufficient conditions for existence of an (n, k) linear code over \(\mathbb {Z}_{p^l}\) correcting the error patterns with respect to the homogeneous weight are derived.
期刊介绍:
TOCS is devoted to publishing original research from all areas of theoretical computer science, ranging from foundational areas such as computational complexity, to fundamental areas such as algorithms and data structures, to focused areas such as parallel and distributed algorithms and architectures.