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<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>

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Some constructions of MDS QECCs and MDS EAQECCs from two classes of GRS codes

  • 期刊论文

  • 发表日期：

    2025年8月23日

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  • Ruhao Wan,
  • Shixin Zhu

摘要

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.