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On the Construction of Quantum MDS Codes

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Abstract

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. The paper is devoted to the construction of new quantum MDS codes based on classical constacyclic codes and cyclic codes over \(\mathbb {F}_{q^{2}}\). We construct a family of new quantum MDS codes with length \(n=\frac {q^{2}+ 1}{a}\), which is a generalization of results in Zhang and Ge (IEEE Trans. Inf. Theory 61(9):5224–5228, 2015), Chen et al. (IEEE. Trans. Inf. Theory 61:1474–1484, 2015). Most of these quantum MDS codes are new in the sense that their parameters are not covered by the quantum codes available in the literature.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their very meticulous reading and valuable comments.

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Authors and Affiliations

  1. Department of Basic Sciences, Air Force Engineering University, Xi’an, Shaanxi, 710051, People’s Republic of China

    Guanmin Guo, Ruihu Li & Luobin Guo

Authors
  1. Guanmin Guo
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  2. Ruihu Li
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  3. Luobin Guo
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Corresponding author

Correspondence to Ruihu Li.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant No.11471011 and Natural Science Foundation of Shaanxi Province under Grant No.2017JQ1032.

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Guo, G., Li, R. & Guo, L. On the Construction of Quantum MDS Codes. Int J Theor Phys 57, 3525–3539 (2018). https://doi.org/10.1007/s10773-018-3867-3

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  • DOI: https://doi.org/10.1007/s10773-018-3867-3

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