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Construction of new entanglement-assisted quantum MDS codes via cyclic codes

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Abstract

Entanglement-assisted quantum error-correcting (EAQEC) codes can be transformed from classical linear codes through entanglement-assisted formalism by loosing the dual-containing condition and using pre-shared entanglement. It has become a challenging task to construct optimal EAQEC codes and determine the required number of pre-shared entanglement pairs. In this work, we explore the structure of \(q^2\)-ary cyclic codes through analyzing two classes of cyclotomic cosets independently. By computing the number of maximally entangled states, we construct three classes of q-ary entanglement-assisted quantum maximum distance separable (EAQMDS) codes. This construction produces new EAQMDS codes with minimum distance more than \(q+1\).

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Acknowledgements

We thank the anonymous referees for their valuable comments and suggestions that helped to improve greatly the quality of this paper. This research work is supported by the National Natural Science Foundation of China under Grant Nos. 61972126, U21A20428, 12171134, 61802102 and 12001002.

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Authors and Affiliations

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

    Hongmei Lu, Xiaoshan Kai & Shixin Zhu

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  1. Hongmei Lu
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  2. Xiaoshan Kai
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  3. Shixin Zhu
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Correspondence to Xiaoshan Kai.

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Lu, H., Kai, X. & Zhu, S. Construction of new entanglement-assisted quantum MDS codes via cyclic codes. Quantum Inf Process 21, 206 (2022). https://doi.org/10.1007/s11128-022-03547-0

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