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On quantum SPC product codes

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Abstract

Some methods have been proposed to construct quantum codes out of classical codes. There is a relationship between quantum codes and codes on the quaternary field. The structure of CSS codes has been raised to construct quantum codes. Most of them are based on the fact that a classical code is self-orthogonal. In this paper, a quantum code is constructed using a suitable permutation-based technique on the parity check matrix of classical codes. Several examples of the new quantum error correcting codes are provided. Single parity check (SPC) product codes have simple decoding algorithms, as well as good decoding efficiency. With this technique, the SPC product codes are used to construct quantum codes.

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Acknowledgements

I am indebted to the anonymous referees for their comments and suggestions that have improved the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

    M. Hivadi

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  1. M. Hivadi
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Correspondence to M. Hivadi.

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Hivadi, M. On quantum SPC product codes. Quantum Inf Process 17, 324 (2018). https://doi.org/10.1007/s11128-018-2095-3

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