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Three new classes of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

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Abstract

Entanglement-assisted quantum error-correcting (EAQEC) codes can be obtained from arbitrary classical linear codes, based on the entanglement-assisted stabilizer formalism. However, how to determine the required number of shared pairs is challenging. In this paper, we first construct three classes of classical linear MDS codes over finite fields by considering generalized Reed–Solomon codes and calculate the dimension of their Hermitian hulls. By using these MDS codes, we then obtain three new classes of EAQEC codes and EAQEC MDS codes, whose maximally entangled states can take various values. Moreover, these EAQEC codes have more flexible lengths.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Lanqiang Li, Shixin Zhu & Li Liu

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  1. Lanqiang Li
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  2. Shixin Zhu
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  3. Li Liu
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Correspondence to Shixin Zhu.

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This research is supported in part by the Fundamental Research Funds for the Central Universities of China Under Grant No. PA2019GDZC0097 and the National Natural Science Foundation of China Under Grant Nos. 61772168, 61572168, 11871187.

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Li, L., Zhu, S. & Liu, L. Three new classes of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes. Quantum Inf Process 18, 366 (2019). https://doi.org/10.1007/s11128-019-2477-1

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