{"title":"用(U|U+V)构造从Aunu生成的[14 8 3]-线性码[7 4 2]-线性码与已知的[7 4 3]汉明码","authors":"Ibrahim Aa, Chun Pb, Kamoh Nm","doi":"10.4172/2168-9679.1000379","DOIUrl":null,"url":null,"abstract":"In this communication, we enumerate the construction of a [ 7 4 2 ]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"39 1","pages":"1-3"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A New [ 14 8 3 ]-Linear Code From the Aunu Generated [ 7 4 2 ] -Linear Code and the Known [7 4 3 ] Hamming Code Using the (U|U+V) Construction\",\"authors\":\"Ibrahim Aa, Chun Pb, Kamoh Nm\",\"doi\":\"10.4172/2168-9679.1000379\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this communication, we enumerate the construction of a [ 7 4 2 ]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.\",\"PeriodicalId\":15007,\"journal\":{\"name\":\"Journal of Applied and Computational Mathematics\",\"volume\":\"39 1\",\"pages\":\"1-3\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Computational Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4172/2168-9679.1000379\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Computational Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4172/2168-9679.1000379","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A New [ 14 8 3 ]-Linear Code From the Aunu Generated [ 7 4 2 ] -Linear Code and the Known [7 4 3 ] Hamming Code Using the (U|U+V) Construction
In this communication, we enumerate the construction of a [ 7 4 2 ]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.
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