{"title":"哪些代码有无4循环的坦纳图?","authors":"T. Halford, K. Chugg, A. Grant","doi":"10.1109/ISIT.2006.261717","DOIUrl":null,"url":null,"abstract":"Let C be an [n, k, d] binary linear code with rate R = k/n and dual Cperp. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pdperp les lfloorradicnp(p-1)+n2/4+n/2rfloor where p = n - k and dperp is the minimum distance of Cperp . By applying this result, it is shown that 4-cycle-free Tanner graphs do not exist for many classical binary linear block codes","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Which Codes Have 4-Cycle-Free Tanner Graphs?\",\"authors\":\"T. Halford, K. Chugg, A. Grant\",\"doi\":\"10.1109/ISIT.2006.261717\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let C be an [n, k, d] binary linear code with rate R = k/n and dual Cperp. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pdperp les lfloorradicnp(p-1)+n2/4+n/2rfloor where p = n - k and dperp is the minimum distance of Cperp . By applying this result, it is shown that 4-cycle-free Tanner graphs do not exist for many classical binary linear block codes\",\"PeriodicalId\":92224,\"journal\":{\"name\":\"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2006.261717\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2006.261717","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
设C是一个[n, k, d]二进制线性码，速率R = k/n，对偶cbp。在这种对应关系中，证明了C可以用一个无4圈的Tanner图表示，只有当pdperp小于lfloorradicnp(p-1)+n2/4+n/2rfloor，其中p = n - k，且dperp是Cperp的最小距离。应用这一结果，证明了许多经典二进制线性分组码不存在无4环Tanner图
Let C be an [n, k, d] binary linear code with rate R = k/n and dual Cperp. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pdperp les lfloorradicnp(p-1)+n2/4+n/2rfloor where p = n - k and dperp is the minimum distance of Cperp . By applying this result, it is shown that 4-cycle-free Tanner graphs do not exist for many classical binary linear block codes
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