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Several families of MDS QECCs and MDS EAQECCs from Hermitian self-orthogonal GRS codes

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Abstract

Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) play significant roles in quantum information theory. In this paper, we construct several new families of MDS QECCs and MDS EAQECCs by utilizing Hermitian self-orthogonal generalized Reed–Solomon codes. These newly obtained MDS QECCs contain some known classes of MDS QECCs as subclasses and some of them have larger minimum distance. In addition, many q-ary MDS QECCs and MDS EAQECCs in our constructions have length exceeding \(q+1\) and minimum distance surpassing \(\frac{q}{2}+1\).

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for their helpful comments and suggestions. The authors would also like to thank the National Natural Science Foundation of China (Grant Nos. 12171134 and U21A20428) for funding this research.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230601, China

    Yang Li, Shixin Zhu & Yanhui Zhang

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  1. Yang Li
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  2. Shixin Zhu
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  3. Yanhui Zhang
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Correspondence to Shixin Zhu.

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This research is supported by the National Natural Science Foundation of China (Grant Nos. 12171134 and U21A20428).

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Li, Y., Zhu, S. & Zhang, Y. Several families of MDS QECCs and MDS EAQECCs from Hermitian self-orthogonal GRS codes. Quantum Inf Process 23, 111 (2024). https://doi.org/10.1007/s11128-024-04319-8

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