{"title":"Around LCD group codes","authors":"Javier de la Cruz, Wolfgang Willems","doi":"10.1007/s10623-024-01451-5","DOIUrl":null,"url":null,"abstract":"<p>In this note we answer some questions on <span>\\(\\text{ LCD }\\)</span> group codes posed in de la Cruz and Willems (Des Codes Cryptogr 86:2065–2073, 2018) and (Vietnam J Math 51:721–729, 2023). Furthermore, over prime fields we determine completely the <i>p</i>-part of the divisor of an <span>\\(\\text{ LCD }\\)</span> group code. In addition we present a natural construction of nearly <span>\\(\\text{ LCD }\\)</span> codes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"38 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-05","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/s10623-024-01451-5","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
Abstract
In this note we answer some questions on \(\text{ LCD }\) group codes posed in de la Cruz and Willems (Des Codes Cryptogr 86:2065–2073, 2018) and (Vietnam J Math 51:721–729, 2023). Furthermore, over prime fields we determine completely the p-part of the divisor of an \(\text{ LCD }\) group code. In addition we present a natural construction of nearly \(\text{ LCD }\) codes.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
