Cristina Fernández-Córdoba, Adrián Torres, Carlos Vela, Mercè Villanueva
{"title":"Computing efficiently a parity-check matrix for Zps-additive codes","authors":"Cristina Fernández-Córdoba, Adrián Torres, Carlos Vela, Mercè Villanueva","doi":"arxiv-2401.05247","DOIUrl":null,"url":null,"abstract":"The Zps-additive codes of length n are subgroups of Zps^n , and can be seen\nas a generalization of linear codes over Z2, Z4, or more general over Z2s . In\nthis paper, we show two methods for computing a parity-check matrix of a\nZps-additive code from a generator matrix of the code in standard form. We also\ncompare the performance of our results implemented in Magma with the current\navailable function in Magma for codes over finite rings in general. A time\ncomplexity analysis is also shown.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2401.05247","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
The Zps-additive codes of length n are subgroups of Zps^n , and can be seen
as a generalization of linear codes over Z2, Z4, or more general over Z2s . In
this paper, we show two methods for computing a parity-check matrix of a
Zps-additive code from a generator matrix of the code in standard form. We also
compare the performance of our results implemented in Magma with the current
available function in Magma for codes over finite rings in general. A time
complexity analysis is also shown.