{"title":"对称Reed-Muller码的局部可纠错性和对偶码","authors":"Wei Yan, Sian-Jheng Lin","doi":"10.1109/ITW48936.2021.9611491","DOIUrl":null,"url":null,"abstract":"Recently, a variant of the Reed-Muller family, called symmetric Reed-Muller codes, was proposed. In this paper, we prove that multivariable symmetric Reed-Muller codes form a class of locally-correctable codes. Then, the dual codes of symmetric Reed-Muller codes are given.","PeriodicalId":325229,"journal":{"name":"2021 IEEE Information Theory Workshop (ITW)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local Correctabilities and Dual Codes of Symmetric Reed–Muller Codes\",\"authors\":\"Wei Yan, Sian-Jheng Lin\",\"doi\":\"10.1109/ITW48936.2021.9611491\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recently, a variant of the Reed-Muller family, called symmetric Reed-Muller codes, was proposed. In this paper, we prove that multivariable symmetric Reed-Muller codes form a class of locally-correctable codes. Then, the dual codes of symmetric Reed-Muller codes are given.\",\"PeriodicalId\":325229,\"journal\":{\"name\":\"2021 IEEE Information Theory Workshop (ITW)\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 IEEE Information Theory Workshop (ITW)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ITW48936.2021.9611491\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 IEEE Information Theory Workshop (ITW)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITW48936.2021.9611491","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Local Correctabilities and Dual Codes of Symmetric Reed–Muller Codes
Recently, a variant of the Reed-Muller family, called symmetric Reed-Muller codes, was proposed. In this paper, we prove that multivariable symmetric Reed-Muller codes form a class of locally-correctable codes. Then, the dual codes of symmetric Reed-Muller codes are given.
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