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New quantum codes constructed from quaternary BCH codes

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Abstract

In this paper, we firstly study construction of new quantum error-correcting codes (QECCs) from three classes of quaternary imprimitive BCH codes. As a result, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing quaternary BCH codes are determined to be much larger than the result given according to Aly et al. (IEEE Trans Inf Theory 53:1183–1188, 2007) for each different code length. Thus, families of new QECCs are newly obtained, and the constructed QECCs have larger distance than those in the previous literature. Secondly, we apply a combinatorial construction to the imprimitive BCH codes with their corresponding primitive counterpart and construct many new linear quantum codes with good parameters, some of which have parameters exceeding the finite Gilbert–Varshamov bound for linear quantum codes.

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Acknowledgments

The authors are indebted to the anonymous reviewers for constructive comments and suggestions on our manuscript, which improve the manuscript significantly.

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Authors and Affiliations

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

    Gen Xu, Ruihu Li, Luobin Guo & Yuena Ma

Authors
  1. Gen Xu
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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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Corresponding author

Correspondence to Gen Xu.

Additional information

This work is supported by National Natural Science Foundation of China under Grant No. 11471011 and Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1023.

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Xu, G., Li, R., Guo, L. et al. New quantum codes constructed from quaternary BCH codes. Quantum Inf Process 15, 4099–4116 (2016). https://doi.org/10.1007/s11128-016-1397-6

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  • DOI: https://doi.org/10.1007/s11128-016-1397-6

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