{"title":"Some constructions of MDS QECCs and MDS EAQECCs from two classes of GRS codes","authors":"Ruhao Wan, Shixin Zhu","doi":"10.1007/s11128-025-04907-2","DOIUrl":null,"url":null,"abstract":"<div><p>Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) have important applications in quantum computing and quantum communication. In this paper, for two given generalized Reed–Solomon (GRS) codes, we construct a new GRS code of larger code lengthand fixed Hermitian hull dimensions. Consequently, we present a new general construction of MDS QECCs and MDS EAQECCs from known ones. Then, based on many currently known Hermitian self-orthogonal GRS codes, we obtain several new classes of MDS QECCs with flexible parameters. Comparing to previously known constructions, we can enrich the flexibility of the code length. Meanwhile, the results in this paper will be helpful in constructing MDS QECCs with distance <i>q</i> and MDS EAQECCs with flexible parameters.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":"24 9","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-025-04907-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) have important applications in quantum computing and quantum communication. In this paper, for two given generalized Reed–Solomon (GRS) codes, we construct a new GRS code of larger code lengthand fixed Hermitian hull dimensions. Consequently, we present a new general construction of MDS QECCs and MDS EAQECCs from known ones. Then, based on many currently known Hermitian self-orthogonal GRS codes, we obtain several new classes of MDS QECCs with flexible parameters. Comparing to previously known constructions, we can enrich the flexibility of the code length. Meanwhile, the results in this paper will be helpful in constructing MDS QECCs with distance q and MDS EAQECCs with flexible parameters.
期刊介绍：
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.
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