{"title":"Two Families of Optimal Quantum Locally Recoverable Codes","authors":"Dengcheng Xie, Shixin Zhu, Zhonghua Sun","doi":"10.1007/s10773-025-05943-5","DOIUrl":null,"url":null,"abstract":"<div><p>Classical locally recoverable codes (classical LRCs) have wide application in large-scale distributed storage systems due to their efficiency in the recovery of localized errors. In order to satisfy the quest for quantum data storage, quantum locally recoverable codes (qLRCs) have been proposed for their relevant and prospective application. Firstly, two families of classical LRCs from subfields and cyclic groups of finite fields are constructed and their duals are proved to be dual-containing. Then two families of optimal qLRCs with regard to the quantum Singleton-like bound on qLRCs are deduced.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 4","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10773-025-05943-5","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Classical locally recoverable codes (classical LRCs) have wide application in large-scale distributed storage systems due to their efficiency in the recovery of localized errors. In order to satisfy the quest for quantum data storage, quantum locally recoverable codes (qLRCs) have been proposed for their relevant and prospective application. Firstly, two families of classical LRCs from subfields and cyclic groups of finite fields are constructed and their duals are proved to be dual-containing. Then two families of optimal qLRCs with regard to the quantum Singleton-like bound on qLRCs are deduced.
期刊介绍：
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.
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