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Quantum synchronizable codes from repeated-root quasi-cyclic codes

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Abstract

Quantum synchronizable codes are generally constructed from cyclic codes. In this paper, we extend the class of codes available for constructing quantum synchronizable codes. We prove how to construct quantum synchronizable codes using quasi-cyclic codes. We present the method for constructing quantum synchronizable codes from two families of repeated-root quasi-cyclic codes. In addition, we also prove the sufficient condition of Euclidean self-orthogonality and the minimum distance lower bound for the repeated-root quasi-cyclic codes with generators of the form (g(x), k(x)) and (f(x), f(x)).

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Funding

This work was supported by the National Natural Science Foundation of China (Grants No. 61972413, 61901525, 62002385) and the National Key R &D Program of China (No. 2021YFB3100100).

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Authors and Affiliations

  1. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhenghzhou, 450001, Henan, China

    Chao Du, Zhi Ma & Yiting Liu

  2. Henan Key Laboratory of Network Cryptography Technology, Zhenghzhou, 450001, Henan, China

    Chao Du, Zhi Ma & Yiting Liu

Authors
  1. Chao Du
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  2. Zhi Ma
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  3. Yiting Liu
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Correspondence to Zhi Ma.

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The authors declared no potential conflicts of interest with respect to the research, author-ship, or publication of this article.

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Communicated by Somphong Jitman.

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Du, C., Ma, Z. & Liu, Y. Quantum synchronizable codes from repeated-root quasi-cyclic codes. Comp. Appl. Math. 42, 161 (2023). https://doi.org/10.1007/s40314-023-02298-7

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  • DOI: https://doi.org/10.1007/s40314-023-02298-7

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