{"title":"误差控制用多项式环F_2^N [X] / (X^N-1)的理想码发生器","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":"{\"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}","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}
On the generators of codes of ideals of the polynomial ring F_2^N [X] / (X^N-1) for error control
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
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
