{"title":"On a class of cyclic codes whose minimum distance exceeds the BCH bound","authors":"V. Lomakov","doi":"10.1109/RED.2012.6338404","DOIUrl":null,"url":null,"abstract":"It is shown that for any prime p and any integer ℓ ≥ 1, there is a cyclic code of length p<sup>2(ℓ+1)</sup> - 1 and dimension p<sup>ℓ+1</sup>(p<sup>ℓ+1</sup> - 2) over the finite field GF(p) whose minimum distance ≥ p + 2ℓ is greater than or equal to the BCH bound p + 2.","PeriodicalId":403644,"journal":{"name":"2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/RED.2012.6338404","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
It is shown that for any prime p and any integer ℓ ≥ 1, there is a cyclic code of length p2(ℓ+1) - 1 and dimension pℓ+1(pℓ+1 - 2) over the finite field GF(p) whose minimum distance ≥ p + 2ℓ is greater than or equal to the BCH bound p + 2.
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