{"title":"NEW QUANTUM CODES DERIVED FROM THE DIRECT PRODUCT OF RINGS, USING CYCLIC CODES OVER THE RING","authors":"Pooja Soni, Manju Pruthi, Arun Kumar Yadav","doi":"10.1016/S0034-4877(24)00027-2","DOIUrl":null,"url":null,"abstract":"<div><p>This research paper discusses the construction of novel and better quantum codes from the direct product of <em>t</em>-copies of ring <em>R</em> (discussed in Section 2), using cyclic codes over <em>R</em> by employing the CSS construction technique. Here, we present an overview of the structure and essential properties of a ring <em>R</em>. Furthermore, we analyze the distance-preserving nature of the Gray map in Subsection 2.1. Here, we also investigate maximum distance separable (MDS) codes by using the concept of quantum singleton defect (QSD), which indicates the overall quality of codes. To demonstrate the practicality of our findings, we provide illustrative examples implemented using the Magma software.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 213-229"},"PeriodicalIF":1.0000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000272","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
This research paper discusses the construction of novel and better quantum codes from the direct product of t-copies of ring R (discussed in Section 2), using cyclic codes over R by employing the CSS construction technique. Here, we present an overview of the structure and essential properties of a ring R. Furthermore, we analyze the distance-preserving nature of the Gray map in Subsection 2.1. Here, we also investigate maximum distance separable (MDS) codes by using the concept of quantum singleton defect (QSD), which indicates the overall quality of codes. To demonstrate the practicality of our findings, we provide illustrative examples implemented using the Magma software.
本研究论文讨论了通过使用 CSS 构建技术，利用环 R 上的循环码，从环 R 的 t 副本的直接乘积（在第 2 节中讨论）构建新颖且更好的量子编码。此外，我们在第 2.1 小节中分析了格雷映射的距离保留性质。在这里，我们还利用量子单子缺陷（QSD）的概念研究了最大距离可分离（MDS）编码，它表示编码的整体质量。为了证明我们研究结果的实用性，我们提供了使用 Magma 软件实现的示例。
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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