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Quantum synchronizable codes from finite rings

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Abstract

In this paper, we provide two methods of constructing quantum synchronizable codes from cyclic or constacyclic codes over finite rings. The first one is derived from the Calderbank-Shor-Steane (briefly, CSS) construction applied to dual-containing codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the constacyclic codes over semi-local rings \({\mathbb {F}}_{p}+v{\mathbb {F}}_{p}\) with \(v^2=v\). By using two methods, concrete examples are presented to construct new quantum synchronizable codes.

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Acknowledgements

This work was supported by Research Funds of Hubei Province under Grant D20144401, and Training Program of Innovation and Entrepreneurship for Undergraduates under Grant S202010500054.

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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

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  1. Hualu Liu
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  2. Xiusheng Liu
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Correspondence to Hualu Liu.

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Liu, H., Liu, X. Quantum synchronizable codes from finite rings. Quantum Inf Process 20, 125 (2021). https://doi.org/10.1007/s11128-021-03058-4

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