{"title":"A systematic construction of self-dual codes","authors":"J. Carlach, A. Otmani","doi":"10.1109/TIT.2003.815814","DOIUrl":null,"url":null,"abstract":"A new coding construction scheme of block codes using short base codes and permutations that enables the construction of binary self-dual codes is presented in Cadic et al. (2001) and Carlach et al. (1999, 2000). The scheme leads to doubly-even (resp,. singly-even) self-dual codes provided the base code is a doubly-even self-dual code and the number of permutations is even (resp., odd). We study the particular case where the base code is the [8, 4, 4] extended Hamming. In this special case, we construct a new [88, 44, 16] extremal doubly-even self-dual code and we give a new unified construction of the five [32, 16, 8] extremal doubly-even self-dual codes.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"13 1","pages":"3005-3009"},"PeriodicalIF":0.0000,"publicationDate":"2003-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Trans. Inf. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TIT.2003.815814","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 17
Abstract
A new coding construction scheme of block codes using short base codes and permutations that enables the construction of binary self-dual codes is presented in Cadic et al. (2001) and Carlach et al. (1999, 2000). The scheme leads to doubly-even (resp,. singly-even) self-dual codes provided the base code is a doubly-even self-dual code and the number of permutations is even (resp., odd). We study the particular case where the base code is the [8, 4, 4] extended Hamming. In this special case, we construct a new [88, 44, 16] extremal doubly-even self-dual code and we give a new unified construction of the five [32, 16, 8] extremal doubly-even self-dual codes.
Cadic et al.(2001)和carach et al.(1999,2000)提出了一种新的利用短基码和置换的分组码编码构造方案，该方案能够构造二进制自对偶码。该方案可实现双平衡。假设基码是双偶自对偶码，并且排列的数目是偶的(例如:奇怪的)。我们研究了基码为[8,4,4]扩展汉明的特殊情况。在这种特殊情况下，构造了一个新的[88,44,16]极值双偶自对偶码，并给出了5个[32,16,8]极值双偶自对偶码的一个新的统一构造。
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