{"title":"$GF（3）$、$GF（11）$和$GF（13）上的新线性码$","authors":"N. Aydin, Derek Foret","doi":"10.13069/JACODESMATH.508968","DOIUrl":null,"url":null,"abstract":"Explicit construction of linear codes with best possible parameters is one of the major and challenging problems in coding theory. Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, are known to contain many codes with best known parameters. Despite the fact that these classes of codes have been extensively searched, we have been able to refine existing search algorithms to discover many new linear codes over the alphabets $\\mathbb{F}_{3}$, $\\mathbb{F}_{11}$, and $\\mathbb{F}_{13}$ with better parameters. A total of 38 new linear codes over the three alphabets are presented.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$\",\"authors\":\"N. Aydin, Derek Foret\",\"doi\":\"10.13069/JACODESMATH.508968\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Explicit construction of linear codes with best possible parameters is one of the major and challenging problems in coding theory. Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, are known to contain many codes with best known parameters. Despite the fact that these classes of codes have been extensively searched, we have been able to refine existing search algorithms to discover many new linear codes over the alphabets $\\\\mathbb{F}_{3}$, $\\\\mathbb{F}_{11}$, and $\\\\mathbb{F}_{13}$ with better parameters. A total of 38 new linear codes over the three alphabets are presented.\",\"PeriodicalId\":37029,\"journal\":{\"name\":\"Journal of Algebra Combinatorics Discrete Structures and Applications\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra Combinatorics Discrete Structures and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13069/JACODESMATH.508968\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra Combinatorics Discrete Structures and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13069/JACODESMATH.508968","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$
Explicit construction of linear codes with best possible parameters is one of the major and challenging problems in coding theory. Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, are known to contain many codes with best known parameters. Despite the fact that these classes of codes have been extensively searched, we have been able to refine existing search algorithms to discover many new linear codes over the alphabets $\mathbb{F}_{3}$, $\mathbb{F}_{11}$, and $\mathbb{F}_{13}$ with better parameters. A total of 38 new linear codes over the three alphabets are presented.
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