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On classical BCH codes and quantum BCH codes

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Journal of Electronics (China)

Abstract

It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.

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Authors and Affiliations

  1. Department of Information Research, PLA Information Engineering University, Zhengzhou, 450002, China

    Yajie Xu & Zhi Ma

Authors
  1. Yajie Xu
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  2. Zhi Ma
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  3. Chunyuan Zhang
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Corresponding author

Correspondence to Yajie Xu.

Additional information

Supported by the National Natural Science Foundation of China (No.60403004), the Outstanding Youth Foundation of China (No.0612000500).

Communication author: Xu Yajie, born in 1984, female, graduate student.

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Xu, Y., Ma, Z. & Zhang, C. On classical BCH codes and quantum BCH codes. J. Electron.(China) 26, 64–70 (2009). https://doi.org/10.1007/s11767-007-0120-2

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  • DOI: https://doi.org/10.1007/s11767-007-0120-2

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