{"title":"On the generators of codes of ideals of the polynomial ring F_2^N [X] / (X^N-1) for error control","authors":"Olege. Fanuel","doi":"10.12988/imf.2019.9732","DOIUrl":null,"url":null,"abstract":"Shannon introduced error detection and correction codes to address the growing need of efficiency and reliability of code vectors. One of the structures that can generate these codes is a set of ideals of the candidate polynomial ring. Generators of codes of ideals of polynomial rings have not been fully characterized. In this research the generators of codes of the candidate polynomial ring Fn 2 [x]/〈xn − 1〉 have been investigated and characterized using lattices, simplex Hamming codes and isometries. Mathematics Subject Classification: Primary 20K30; Secondary 16P10","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/imf.2019.9732","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Shannon introduced error detection and correction codes to address the growing need of efficiency and reliability of code vectors. One of the structures that can generate these codes is a set of ideals of the candidate polynomial ring. Generators of codes of ideals of polynomial rings have not been fully characterized. In this research the generators of codes of the candidate polynomial ring Fn 2 [x]/〈xn − 1〉 have been investigated and characterized using lattices, simplex Hamming codes and isometries. Mathematics Subject Classification: Primary 20K30; Secondary 16P10
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