{"title":"ZPm环上线性循环码的深度谱","authors":"Xiying Zheng, Bo Kong","doi":"10.1109/YCICT.2010.5713070","DOIUrl":null,"url":null,"abstract":"In this paper, the generator polynomial of linear cyclic codes on ring Z<inf>Pm</inf> are studied, and we prove that the depth spectrum of linear cyclic codes C<inf>l</inf> = (p<sup>l−1</sup>f<inf>l</inf>)(degf<inf>l</inf> = n−k, l = 1, 2 · · · ,m) has consisted exactly k non zero values and give the depth spectrum of linear cyclic codes on ring Z<inf>Pm</inf>.","PeriodicalId":179847,"journal":{"name":"2010 IEEE Youth Conference on Information, Computing and Telecommunications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The depth spectrums of linear cyclic codes on ring ZPm\",\"authors\":\"Xiying Zheng, Bo Kong\",\"doi\":\"10.1109/YCICT.2010.5713070\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the generator polynomial of linear cyclic codes on ring Z<inf>Pm</inf> are studied, and we prove that the depth spectrum of linear cyclic codes C<inf>l</inf> = (p<sup>l−1</sup>f<inf>l</inf>)(degf<inf>l</inf> = n−k, l = 1, 2 · · · ,m) has consisted exactly k non zero values and give the depth spectrum of linear cyclic codes on ring Z<inf>Pm</inf>.\",\"PeriodicalId\":179847,\"journal\":{\"name\":\"2010 IEEE Youth Conference on Information, Computing and Telecommunications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 IEEE Youth Conference on Information, Computing and Telecommunications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/YCICT.2010.5713070\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE Youth Conference on Information, Computing and Telecommunications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/YCICT.2010.5713070","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了ZPm环上线性循环码的生成多项式,证明了线性循环码的深度谱Cl = (pl−1fl)(degfl = n−k, l = 1,2···,m)恰好由k个非零值组成,并给出了ZPm环上线性循环码的深度谱。
The depth spectrums of linear cyclic codes on ring ZPm
In this paper, the generator polynomial of linear cyclic codes on ring ZPm are studied, and we prove that the depth spectrum of linear cyclic codes Cl = (pl−1fl)(degfl = n−k, l = 1, 2 · · · ,m) has consisted exactly k non zero values and give the depth spectrum of linear cyclic codes on ring ZPm.