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Entanglement-assisted quantum MDS codes from negacyclic codes

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Abstract

The entanglement-assisted formalism generalizes the standard stabilizer formalism, which can transform arbitrary classical linear codes into entanglement-assisted quantum error-correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we construct six classes of q-ary entanglement-assisted quantum MDS (EAQMDS) codes based on classical negacyclic MDS codes by exploiting two or more pre-shared maximally entangled states. We show that two of these six classes q-ary EAQMDS have minimum distance more larger than \(q+1\). Most of these q-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.

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Acknowledgements

This work is supported by National Natural Science Foundations of China under Grant No. 11471011 and the Natural Science Foundation of Shaanxi under Grant No. 2017JQ1032. We are grateful to the two anonymous reviewers for their helpful and constructive comments.

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Authors and Affiliations

  1. School of Science, Air Force Engineering University, Xi’an, 710051, Shaanxi, People’s Republic of China

    Liangdong Lu, Ruihu Li, Luobin Guo, Yuena Ma & Yang Liu

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  1. Liangdong Lu
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  2. Ruihu Li
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  3. Luobin Guo
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  4. Yuena Ma
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  5. Yang Liu
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Correspondence to Liangdong Lu.

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Lu, L., Li, R., Guo, L. et al. Entanglement-assisted quantum MDS codes from negacyclic codes. Quantum Inf Process 17, 69 (2018). https://doi.org/10.1007/s11128-018-1838-5

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