{"title":"ON THE CYCLIC DNA CODES OVER THE FINITE RING","authors":"Y. Cengellenmis, A. Dertli","doi":"10.17114/j.aua.2019.58.01","DOIUrl":null,"url":null,"abstract":"In this paper, the cyclic DNA codes over the finite ring R = F2 + uF2 + vF2 + wF2 + uvF2 + uwF2 + vwF2 + uvwF2, where u 2 = 0, v2 = v, w2 = w, uv = vu, uw = wu, vw = wv are designed. A map from R to R2 1, where R1 = F2 + uF2 + vF2 + uvF2 with u 2 = 0, v2 = v, uv = vu is given. The cyclic codes of arbitrary length over R satisfy the reverse constraint and reverse complement constraint are studied. A one to one correspondence between the elements of the ring R and SD256 is established, where SD256 = {AAAA, ..., GGGG}. The binary image of a cyclic DNA code over the finite ring R is determined. 2010 Mathematics Subject Classification: 94B05, 94B15, 92D10.","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"80 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Universitatis Apulensis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17114/j.aua.2019.58.01","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, the cyclic DNA codes over the finite ring R = F2 + uF2 + vF2 + wF2 + uvF2 + uwF2 + vwF2 + uvwF2, where u 2 = 0, v2 = v, w2 = w, uv = vu, uw = wu, vw = wv are designed. A map from R to R2 1, where R1 = F2 + uF2 + vF2 + uvF2 with u 2 = 0, v2 = v, uv = vu is given. The cyclic codes of arbitrary length over R satisfy the reverse constraint and reverse complement constraint are studied. A one to one correspondence between the elements of the ring R and SD256 is established, where SD256 = {AAAA, ..., GGGG}. The binary image of a cyclic DNA code over the finite ring R is determined. 2010 Mathematics Subject Classification: 94B05, 94B15, 92D10.
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