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Some entanglement-assisted quantum MDS codes with large minimum distance

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Abstract

The construction of quantum maximum-distance-separable (MDS) error-correcting codes has become one of the hot topics in quantum coding theory. In this paper, based on classical Hermitian self-orthogonal generalized Reed–Solomon (GRS) codes, we construct some quantum MDS codes with large minimum distance. In addition, we obtain several families of MDS entanglement-assisted quantum error-correcting codes (EAQECCs) with flexible parameters. Notably, some of the distance parameters of our codes are greater than \(\frac{q}{2}+1\).

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Acknowledgements

We are grateful to the anonymous referees for useful comments and suggestions that improved the presentation and quality of this paper.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Guohui Wang & Chunming Tang

  2. School of Mathematics and Physics, Qinghai University, Xining, 810016, China

    Guohui Wang

  3. Guangdong Provincial Key Laboratory of Information Security Technology, Guangzhou, 510006, China

    Chunming Tang

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  1. Guohui Wang
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  2. Chunming Tang
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Correspondence to Chunming Tang.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 12171114)

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Wang, G., Tang, C. Some entanglement-assisted quantum MDS codes with large minimum distance. Quantum Inf Process 21, 286 (2022). https://doi.org/10.1007/s11128-022-03635-1

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