{"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}
引用次数: 29
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.