{"title":"F_2+uF_2+vF_2上的常环码和负环码及F_2上码的等价","authors":"M. Özkan, Berk Yeni̇ce, Ayşe Tuğba Güroğlu","doi":"10.33401/fujma.1124502","DOIUrl":null,"url":null,"abstract":"In this work, we consider the finite ring F_2 +uF_2 +vF_2, u^2 = 1;v^2 = 0, u.v = v.u = 0 which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes over F_2+uF_2+vF_2 of odd length. These codes are compared with codes that had priorly been obtained on the finite field F_2. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over F_2+uF_2+vF_2 of odd length n is a quasicyclic code of index 4 with length 4n over F_2. In particular, the Gray images are applied to two different rings S_1 = F_2+vF_2, v^2 = 0 and S_2 = F_2+uF_2, u^2 = 1 and negacyclic and constacyclic images of these rings are also discussed.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Constacyclic and Negacyclic Codes over F_2+uF_2+vF_2 and Equivalents of Codes in F_2\",\"authors\":\"M. Özkan, Berk Yeni̇ce, Ayşe Tuğba Güroğlu\",\"doi\":\"10.33401/fujma.1124502\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we consider the finite ring F_2 +uF_2 +vF_2, u^2 = 1;v^2 = 0, u.v = v.u = 0 which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes over F_2+uF_2+vF_2 of odd length. These codes are compared with codes that had priorly been obtained on the finite field F_2. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over F_2+uF_2+vF_2 of odd length n is a quasicyclic code of index 4 with length 4n over F_2. In particular, the Gray images are applied to two different rings S_1 = F_2+vF_2, v^2 = 0 and S_2 = F_2+uF_2, u^2 = 1 and negacyclic and constacyclic images of these rings are also discussed.\",\"PeriodicalId\":199091,\"journal\":{\"name\":\"Fundamental Journal of Mathematics and Applications\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamental Journal of Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33401/fujma.1124502\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Journal of Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33401/fujma.1124502","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Constacyclic and Negacyclic Codes over F_2+uF_2+vF_2 and Equivalents of Codes in F_2
In this work, we consider the finite ring F_2 +uF_2 +vF_2, u^2 = 1;v^2 = 0, u.v = v.u = 0 which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes over F_2+uF_2+vF_2 of odd length. These codes are compared with codes that had priorly been obtained on the finite field F_2. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over F_2+uF_2+vF_2 of odd length n is a quasicyclic code of index 4 with length 4n over F_2. In particular, the Gray images are applied to two different rings S_1 = F_2+vF_2, v^2 = 0 and S_2 = F_2+uF_2, u^2 = 1 and negacyclic and constacyclic images of these rings are also discussed.
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