{"title":"II型代码通过F2 + uF2 + u2F2","authors":"Jia Qian, Lina Zhang, Zhixiang Yin","doi":"10.1109/ITW2.2006.323744","DOIUrl":null,"url":null,"abstract":"Motivated by the work of Dougherty, Ling and Betsumiya, we define type II codes over R = F<sub>2</sub> + uF<sub>2</sub> + u<sup>2</sup>F <sub>2</sub> as self-dual codes with Lee weights a multiple of 4. A new Gray map between codes over R and codes over F<sub>2</sub> is defined. The existence of self-dual code over R is examined. Properties of the Gray map which take self-dual codes over R to self-dual codes over F<sub>2</sub> are studied","PeriodicalId":299513,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Chengdu","volume":"6 5","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Type II code over F2 + uF2 + u2F2\",\"authors\":\"Jia Qian, Lina Zhang, Zhixiang Yin\",\"doi\":\"10.1109/ITW2.2006.323744\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by the work of Dougherty, Ling and Betsumiya, we define type II codes over R = F<sub>2</sub> + uF<sub>2</sub> + u<sup>2</sup>F <sub>2</sub> as self-dual codes with Lee weights a multiple of 4. A new Gray map between codes over R and codes over F<sub>2</sub> is defined. The existence of self-dual code over R is examined. Properties of the Gray map which take self-dual codes over R to self-dual codes over F<sub>2</sub> are studied\",\"PeriodicalId\":299513,\"journal\":{\"name\":\"2006 IEEE Information Theory Workshop - ITW '06 Chengdu\",\"volume\":\"6 5\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 IEEE Information Theory Workshop - ITW '06 Chengdu\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ITW2.2006.323744\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 IEEE Information Theory Workshop - ITW '06 Chengdu","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITW2.2006.323744","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Motivated by the work of Dougherty, Ling and Betsumiya, we define type II codes over R = F2 + uF2 + u2F 2 as self-dual codes with Lee weights a multiple of 4. A new Gray map between codes over R and codes over F2 is defined. The existence of self-dual code over R is examined. Properties of the Gray map which take self-dual codes over R to self-dual codes over F2 are studied
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