{"title":"An Open Problem and a Conjecture on Binary Linear Complementary Pairs of Codes","authors":"Shitao Li;Minjia Shi;San Ling","doi":"10.1109/TIT.2024.3443090","DOIUrl":null,"url":null,"abstract":"Carlet et al. showed that for \n<inline-formula> <tex-math>$q\\gt 2$ </tex-math></inline-formula>\n, there exists a q-ary linear complementary pair (LCP) of codes whose security parameter is as good as the minimum distance of the best linear code with the same length and dimension. In this paper, we study the best security parameters of binary LCPs of codes. As a result, we solve an open problem proposed by Carlet et al. (IEEE Trans. Inf. Theory 65(3): 1694-1704, 2019) and a conjecture proposed by Choi et al. (Cryptogr. Commun. 15(2): 469-486, 2023).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"219-226"},"PeriodicalIF":2.9000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Information Theory","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10634515/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Carlet et al. showed that for
$q\gt 2$
, there exists a q-ary linear complementary pair (LCP) of codes whose security parameter is as good as the minimum distance of the best linear code with the same length and dimension. In this paper, we study the best security parameters of binary LCPs of codes. As a result, we solve an open problem proposed by Carlet et al. (IEEE Trans. Inf. Theory 65(3): 1694-1704, 2019) and a conjecture proposed by Choi et al. (Cryptogr. Commun. 15(2): 469-486, 2023).
期刊介绍：
The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.
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