{"title":"线性码的子集子码","authors":"A. Urivskiy","doi":"10.1109/RED.2012.6338415","DOIUrl":null,"url":null,"abstract":"We consider a problem of finding codes over alphabets whose size s is not equal to the size of any finite field. We adopted an approach when a linear block code is taken over some finite field GF(q) such that q >; s. Then a subcode is being found such that all the code symbols of all its codewords belong to a subset of GF(q) of size s. Upper and lower bounds on the cardinality of the subset subcode are given. Also coding procedures are considered. Error detection and/or correction procedures are those of the parent code.","PeriodicalId":403644,"journal":{"name":"2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On subset subcodes of linear codes\",\"authors\":\"A. Urivskiy\",\"doi\":\"10.1109/RED.2012.6338415\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a problem of finding codes over alphabets whose size s is not equal to the size of any finite field. We adopted an approach when a linear block code is taken over some finite field GF(q) such that q >; s. Then a subcode is being found such that all the code symbols of all its codewords belong to a subset of GF(q) of size s. Upper and lower bounds on the cardinality of the subset subcode are given. Also coding procedures are considered. Error detection and/or correction procedures are those of the parent code.\",\"PeriodicalId\":403644,\"journal\":{\"name\":\"2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/RED.2012.6338415\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/RED.2012.6338415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider a problem of finding codes over alphabets whose size s is not equal to the size of any finite field. We adopted an approach when a linear block code is taken over some finite field GF(q) such that q >; s. Then a subcode is being found such that all the code symbols of all its codewords belong to a subset of GF(q) of size s. Upper and lower bounds on the cardinality of the subset subcode are given. Also coding procedures are considered. Error detection and/or correction procedures are those of the parent code.
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