{"title":"Bounds and constructions of optimal symbol-pair codes with constant pair-weight","authors":"Mengzhen Zhao, Yanxun Chang","doi":"10.1007/s10623-025-01598-9","DOIUrl":null,"url":null,"abstract":"<p>Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against pair errors in symbol-pair read channels. This special channel structure is motivated by the limitations of the reading process in high density data storage systems, where it is no longer possible to read individual symbols. In this work, we study bounds and constructions of codes in symbol-pair metric. By using some combinatorial structures, we give constructions of optimal <i>q</i>-ary symbol-pair codes with constant pair-weight <span>\\(w_p\\)</span> and pair-distance <span>\\(2w_p-1\\)</span> for some length <i>n</i>, and some optimal <i>q</i>-ary codes with pair-weight <span>\\(w_p=3,4\\)</span> for all pair-distance between 3 and <span>\\(2w_p-1\\)</span>.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"28 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-02-22","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/s10623-025-01598-9","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
Abstract
Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against pair errors in symbol-pair read channels. This special channel structure is motivated by the limitations of the reading process in high density data storage systems, where it is no longer possible to read individual symbols. In this work, we study bounds and constructions of codes in symbol-pair metric. By using some combinatorial structures, we give constructions of optimal q-ary symbol-pair codes with constant pair-weight \(w_p\) and pair-distance \(2w_p-1\) for some length n, and some optimal q-ary codes with pair-weight \(w_p=3,4\) for all pair-distance between 3 and \(2w_p-1\).
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.
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