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Entanglement-assisted quantum MDS codes constructed from negacyclic codes

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Abstract

Recently, entanglement-assisted quantum codes have been constructed from cyclic codes by some scholars. However, how to determine the number of shared pairs required to construct entanglement-assisted quantum codes is not an easy work. In this paper, we propose a decomposition of the defining set of negacyclic codes. Based on this method, four families of entanglement-assisted quantum codes constructed in this paper satisfy the entanglement-assisted quantum Singleton bound, where the minimum distance satisfies \(q+1 \le d\le \frac{n+2}{2}\). Furthermore, we construct two families of entanglement-assisted quantum codes with maximal entanglement.

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Acknowledgements

We are indebted to anonymous reviewers who have made constructive suggestions for the improvement of this manuscript. The research was supported by the Natural Science Foundation of Fujian Province, China (Nos. 2016J01281, 2016J01278) and Foundation of Fujian Agriculture and Forestry University (61201406304).

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Authors and Affiliations

  1. College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou, 350002, China

    Jianzhang Chen, Chunhui Feng & Riqing Chen

  2. Department of Network Engineering, Chengdu University of Information Technology, Chengdu, 610225, China

    Yuanyuan Huang

Authors
  1. Jianzhang Chen
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  2. Yuanyuan Huang
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  3. Chunhui Feng
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  4. Riqing Chen
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Correspondence to Yuanyuan Huang.

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Chen, J., Huang, Y., Feng, C. et al. Entanglement-assisted quantum MDS codes constructed from negacyclic codes. Quantum Inf Process 16, 303 (2017). https://doi.org/10.1007/s11128-017-1750-4

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