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New asymmetric quantum codes from matrix-product codes

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Abstract

In this paper, we provide the method of constructing asymmetric quantum codes by means of the Euclidean sums of matrix-product codes over finite fields. We construct asymmetric quantum codes of length 2n by using the Euclidean sums of matrix-product codes whose constituent codes are Reed–Solomon codes, and asymmetric quantum codes of length 3n by using the Euclidean sums of matrix-product codes whose constituent codes are generated by Fourier matrices. Using these constructions, concrete examples are presented to construct new asymmetric quantum codes. In addition, our obtained asymmetric quantum codes have better parameters than the ones available in the literature.

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Acknowledgements

This work was supported by Research Funds of Hubei Province (Grant No. Q20164505) and the talent project of Hubei Polytechnic University of China (Grant No. 16xjzo8R).

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Authors and Affiliations

  1. School of Science, Hubei University of Technology, Wuhan, 430068, Hubei, China

    Hualu Liu

  2. School of Science and Technology, College of Arts and Science of Hubei Normal University, Huangshi, 435109, Hubei, China

    Xiusheng Liu

  3. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006, Guangdong, China

    Yuan Yuan

Authors
  1. Hualu Liu
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  2. Xiusheng Liu
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  3. Yuan Yuan
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Contributions

Hualu Liu constructed asymmetric quantum codes of length 2n by using the Euclidean sums of matrix-product codes over F_q. Xiusheng Liu used the computer algebra system MAGMA to find more new good asymmetric quantum codes. Yuan Yuan provided three classes of asymmetric quantum codes with good parameters via Fourier matrix.

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Correspondence to Yuan Yuan.

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Liu, H., Liu, X. & Yuan, Y. New asymmetric quantum codes from matrix-product codes. Quantum Inf Process 23, 229 (2024). https://doi.org/10.1007/s11128-024-04445-3

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  • DOI: https://doi.org/10.1007/s11128-024-04445-3

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