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Construction of punctured and extended quantum codes over GF(2)

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Abstract

On the basis of elementary transformation, we propose a new method for constructing a class of pure quantum codes [[n − i, 2k − n + i, d − i]]2 and [[n + 1, 2k − n − 1, d + 1]]2 from a class of classical linear codes [n, k, d]2 that contain their dual codes. The construction process was based on the elementary algebra; the error-correcting performance of the quantum codes was analyzed according to the relationship between the parity-check matrix and the minimum distance of the classical linear codes; the encoding and decoding networks were constructed based on the stabilizer. The proposed method is simple, straightforward and easy to implement using a computer and other hardware system. The theoretical results showed that the method is practical for the construction of a class of quantum codes.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Southeast University, Nanjing, 211189, China

    FangYing Xiao, HanWu Chen, MeiJu Xing & ZhiHao Liu

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  1. FangYing Xiao
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  2. HanWu Chen
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  3. MeiJu Xing
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  4. ZhiHao Liu
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Correspondence to HanWu Chen.

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Xiao, F., Chen, H., Xing, M. et al. Construction of punctured and extended quantum codes over GF(2). Sci. China Inf. Sci. 56, 1–11 (2013). https://doi.org/10.1007/s11432-012-4596-5

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  • DOI: https://doi.org/10.1007/s11432-012-4596-5

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