{"title":"可交换有限局部环上若干矩阵和自由线性码的枚举","authors":"S. Sirisuk","doi":"10.1515/spma-2021-0150","DOIUrl":null,"url":null,"abstract":"Abstract Let R be a commutative finite local ring. Two enumeration problems over R are presented. We enumerate the matrices over R with a given McCoy rank and a given number of rows of single unit, and the free linear codes over R which have a given rank and a given number of vectors of single unit.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"109 - 116"},"PeriodicalIF":0.8000,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Enumeration of some matrices and free linear codes over commutative finite local rings\",\"authors\":\"S. Sirisuk\",\"doi\":\"10.1515/spma-2021-0150\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let R be a commutative finite local ring. Two enumeration problems over R are presented. We enumerate the matrices over R with a given McCoy rank and a given number of rows of single unit, and the free linear codes over R which have a given rank and a given number of vectors of single unit.\",\"PeriodicalId\":43276,\"journal\":{\"name\":\"Special Matrices\",\"volume\":\"10 1\",\"pages\":\"109 - 116\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Special Matrices\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/spma-2021-0150\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Special Matrices","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/spma-2021-0150","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Enumeration of some matrices and free linear codes over commutative finite local rings
Abstract Let R be a commutative finite local ring. Two enumeration problems over R are presented. We enumerate the matrices over R with a given McCoy rank and a given number of rows of single unit, and the free linear codes over R which have a given rank and a given number of vectors of single unit.
期刊介绍：
Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.
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