{"title":"解剖和定重规范","authors":"V. Vaishampayan, N. Sloane","doi":"10.1109/ITW2.2006.323743","DOIUrl":null,"url":null,"abstract":"The problem of encoding and decoding binary block codes of length n and constant Hamming weight w is formulated as a polytope dissection problem. This is done by working with a w-dimensional Euclidean space representation for the information and code vectors. Novel algorithms based on two new dissections are presented. The first is a dissection of a subset of the codebook, and has time-complexity o(w). The second is a dissection of the entire codebook, and has time-complexity o(w log w). Implementation issues associated with the second algorithm are discussed in detail","PeriodicalId":299513,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Chengdu","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Dissections and Constant Weight Codes\",\"authors\":\"V. Vaishampayan, N. Sloane\",\"doi\":\"10.1109/ITW2.2006.323743\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of encoding and decoding binary block codes of length n and constant Hamming weight w is formulated as a polytope dissection problem. This is done by working with a w-dimensional Euclidean space representation for the information and code vectors. Novel algorithms based on two new dissections are presented. The first is a dissection of a subset of the codebook, and has time-complexity o(w). The second is a dissection of the entire codebook, and has time-complexity o(w log w). Implementation issues associated with the second algorithm are discussed in detail\",\"PeriodicalId\":299513,\"journal\":{\"name\":\"2006 IEEE Information Theory Workshop - ITW '06 Chengdu\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 IEEE Information Theory Workshop - ITW '06 Chengdu\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ITW2.2006.323743\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 IEEE Information Theory Workshop - ITW '06 Chengdu","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITW2.2006.323743","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
将长度为n、恒汉明权值为w的二进制分组码的编解码问题表述为多面体解剖问题。这是通过使用信息和代码向量的w维欧几里德空间表示来完成的。提出了基于两种新的解剖的新算法。第一种是对码本子集的剖析，其时间复杂度为0 (w)。第二种是对整个码本的解剖，其时间复杂度为0 (w log w)。详细讨论了与第二种算法相关的实现问题
The problem of encoding and decoding binary block codes of length n and constant Hamming weight w is formulated as a polytope dissection problem. This is done by working with a w-dimensional Euclidean space representation for the information and code vectors. Novel algorithms based on two new dissections are presented. The first is a dissection of a subset of the codebook, and has time-complexity o(w). The second is a dissection of the entire codebook, and has time-complexity o(w log w). Implementation issues associated with the second algorithm are discussed in detail
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