{"title":"作为广义Reed-Muller码生成器的最小权码字","authors":"Peng Ding, J. D. Key","doi":"10.1109/18.868484","DOIUrl":null,"url":null,"abstract":"We establish the range of values of /spl rho/, where 0/spl les//spl rho//spl les/m(q-1), for which the generalized Reed-Muller code R/sub Fq/(/spl rho/, m) of length q/sup m/ over the field F/sub q/ of order q is spanned by its minimum-weight vectors.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"141 1","pages":"2152-2158"},"PeriodicalIF":0.0000,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":"{\"title\":\"Minimum-weight codewords as generators of generalized Reed-Muller codes\",\"authors\":\"Peng Ding, J. D. Key\",\"doi\":\"10.1109/18.868484\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish the range of values of /spl rho/, where 0/spl les//spl rho//spl les/m(q-1), for which the generalized Reed-Muller code R/sub Fq/(/spl rho/, m) of length q/sup m/ over the field F/sub q/ of order q is spanned by its minimum-weight vectors.\",\"PeriodicalId\":13250,\"journal\":{\"name\":\"IEEE Trans. Inf. Theory\",\"volume\":\"141 1\",\"pages\":\"2152-2158\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"29\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Trans. Inf. Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/18.868484\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Trans. Inf. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/18.868484","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Minimum-weight codewords as generators of generalized Reed-Muller codes
We establish the range of values of /spl rho/, where 0/spl les//spl rho//spl les/m(q-1), for which the generalized Reed-Muller code R/sub Fq/(/spl rho/, m) of length q/sup m/ over the field F/sub q/ of order q is spanned by its minimum-weight vectors.
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