{"title":"Reed-Muller码和Barnes-Wall格的广义多层结构","authors":"A. Salomon, O. Amrani","doi":"10.1109/ISIT.2006.261788","DOIUrl":null,"url":null,"abstract":"Generalized multilevel constructions for binary Reed-Muller R(r,m) codes using projections onto GF(2q) are presented. These constructions exploit component codes over GF(2),GF(4),...,GF(2q ) that are based on shorter Reed-Muller codes, and set partitioning using partition chains of length-2l codes. This is then used for deriving multilevel constructions for the Barnes-Wall A(r, m) family of lattices. Similarly, the latter construction involves component codes over GF(2),GF(4),...,GF(2q) and set partitioning based on partition chains of length-2l lattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Multilevel Constructions for Reed-Muller Codes and Barnes-Wall lattices\",\"authors\":\"A. Salomon, O. Amrani\",\"doi\":\"10.1109/ISIT.2006.261788\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Generalized multilevel constructions for binary Reed-Muller R(r,m) codes using projections onto GF(2q) are presented. These constructions exploit component codes over GF(2),GF(4),...,GF(2q ) that are based on shorter Reed-Muller codes, and set partitioning using partition chains of length-2l codes. This is then used for deriving multilevel constructions for the Barnes-Wall A(r, m) family of lattices. Similarly, the latter construction involves component codes over GF(2),GF(4),...,GF(2q) and set partitioning based on partition chains of length-2l lattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding\",\"PeriodicalId\":115298,\"journal\":{\"name\":\"2006 IEEE International Symposium on Information Theory\",\"volume\":\"34 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 IEEE International Symposium on Information Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2006.261788\",\"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 International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2006.261788","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalized Multilevel Constructions for Reed-Muller Codes and Barnes-Wall lattices
Generalized multilevel constructions for binary Reed-Muller R(r,m) codes using projections onto GF(2q) are presented. These constructions exploit component codes over GF(2),GF(4),...,GF(2q ) that are based on shorter Reed-Muller codes, and set partitioning using partition chains of length-2l codes. This is then used for deriving multilevel constructions for the Barnes-Wall A(r, m) family of lattices. Similarly, the latter construction involves component codes over GF(2),GF(4),...,GF(2q) and set partitioning based on partition chains of length-2l lattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding
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