{"title":"On linear codes over a non-chain extension of F2 + uF2","authors":"B. Srinivasulu, Maheshanand Bhaintwal","doi":"10.1109/C3IT.2015.7060155","DOIUrl":null,"url":null,"abstract":"In this paper we study linear codes over a new ring R = F<sub>2</sub> + uF<sub>2</sub> + vF<sub>2</sub> + uvF<sub>2</sub> with u<sup>2</sup> = 0, v<sup>2</sup> = v and uv = vu, which is a non chain extension of the ring F<sub>2</sub>+uF<sub>2</sub>, u<sup>2</sup> =0. We have obtained Mac Williams identities for Lee weight enumerator of linear codes over R using a Gray map from R<sup>n</sup> to (F<sub>2</sub> +uF<sub>2</sub>)<sup>n</sup>. We have studied self-dual codes over R and determined some existential conditions for Type I and Type II codes over R. Further we have briefly studied cyclic codes over R. It is shown that R[x]/〈x<sup>n</sup> - 1〉 is a PIR when n is odd. The form of the generator of a cyclic code of odd length over R is obtained.","PeriodicalId":402311,"journal":{"name":"Proceedings of the 2015 Third International Conference on Computer, Communication, Control and Information Technology (C3IT)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2015 Third International Conference on Computer, Communication, Control and Information Technology (C3IT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/C3IT.2015.7060155","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
In this paper we study linear codes over a new ring R = F2 + uF2 + vF2 + uvF2 with u2 = 0, v2 = v and uv = vu, which is a non chain extension of the ring F2+uF2, u2 =0. We have obtained Mac Williams identities for Lee weight enumerator of linear codes over R using a Gray map from Rn to (F2 +uF2)n. We have studied self-dual codes over R and determined some existential conditions for Type I and Type II codes over R. Further we have briefly studied cyclic codes over R. It is shown that R[x]/〈xn - 1〉 is a PIR when n is odd. The form of the generator of a cyclic code of odd length over R is obtained.
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