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Two new families of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

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Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC by any classical linear code. In this paper, we propose two constructions of generalized Reed–Solomon codes and calculate the dimension of their hulls. With these generalized Reed–Solomon codes, we present two new infinite families of EAQECCs, which are optimal with respect to the Singleton bound for EAQECCs. Notably, the parameters of our EAQECCs are new and flexible.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, China

    Gaojun Luo & Xiwang Cao

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Xiwang Cao

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  1. Gaojun Luo
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  2. Xiwang Cao
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Correspondence to Gaojun Luo.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11771007 and 61572027) and the China Scholarship Council (201806830044).

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Luo, G., Cao, X. Two new families of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes. Quantum Inf Process 18, 89 (2019). https://doi.org/10.1007/s11128-019-2207-8

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