{"title":"Optimal Asymmetric Quantum Codes from the Euclidean Sums of Linear Codes","authors":"Peng Xu, Xiusheng Liu","doi":"10.1051/wujns/2024291045","DOIUrl":null,"url":null,"abstract":"In this paper, we first give the definition of the Euclidean sums of linear codes, and prove that the Euclidean sums of linear codes are Euclidean dual-containing. Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes, and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields. Moreover, these optimal asymmetric quantum error-correcting codes constructed in this paper are different from the ones in the literature.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wuhan University Journal of Natural Sciences","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.1051/wujns/2024291045","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Multidisciplinary","Score":null,"Total":0}
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Abstract
In this paper, we first give the definition of the Euclidean sums of linear codes, and prove that the Euclidean sums of linear codes are Euclidean dual-containing. Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes, and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields. Moreover, these optimal asymmetric quantum error-correcting codes constructed in this paper are different from the ones in the literature.
期刊介绍：
Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.
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