{"title":"Quaternary Reed – Muller codes and their minimum weight bases","authors":"F. Solov'eva","doi":"10.1109/REDUNDANCY52534.2021.9606466","DOIUrl":null,"url":null,"abstract":"We prove that the families of quaternary Reed – Muller codes obtained by the BQ-Plotkin construction 2009 have bases of minimum weight codewords. In 2020 we found that the quaternary Reed – Muller codes constructed by the quaternary Plotkin approach have the minimum weight bases. Combining these two constructions we prove that all known quaternary linear Reed – Muller codes have bases of minimum weight codewords. The bases are obtained iteratively.","PeriodicalId":408692,"journal":{"name":"2021 XVII International Symposium \"Problems of Redundancy in Information and Control Systems\" (REDUNDANCY)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 XVII International Symposium \"Problems of Redundancy in Information and Control Systems\" (REDUNDANCY)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/REDUNDANCY52534.2021.9606466","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
We prove that the families of quaternary Reed – Muller codes obtained by the BQ-Plotkin construction 2009 have bases of minimum weight codewords. In 2020 we found that the quaternary Reed – Muller codes constructed by the quaternary Plotkin approach have the minimum weight bases. Combining these two constructions we prove that all known quaternary linear Reed – Muller codes have bases of minimum weight codewords. The bases are obtained iteratively.
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