{"title":"On algebraic decoding of the Z4-linear Goethals-like codes","authors":"K. Ranto","doi":"10.1109/18.868490","DOIUrl":null,"url":null,"abstract":"The Z/sub 4/-linear Goethals-like code of length 2/sup m/ has 2/sup 2m+1-3m-2/ codewords and minimum Lee distance 8 for any odd integer m/spl ges/3. We present an algebraic decoding algorithm for all Z/sub 4/-linear Goethals-like codes C/sub k/ introduced by Helleseth et al.(1995, 1996). We use Dickson polynomials and their properties to solve the syndrome equations.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"42 1","pages":"2193-2197"},"PeriodicalIF":0.0000,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Trans. Inf. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/18.868490","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
The Z/sub 4/-linear Goethals-like code of length 2/sup m/ has 2/sup 2m+1-3m-2/ codewords and minimum Lee distance 8 for any odd integer m/spl ges/3. We present an algebraic decoding algorithm for all Z/sub 4/-linear Goethals-like codes C/sub k/ introduced by Helleseth et al.(1995, 1996). We use Dickson polynomials and their properties to solve the syndrome equations.
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