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QSCs from the Euclidean sums of cyclic codes over finite rings

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Abstract

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes that can correct the effects of both quantum noise on qubits and misalignment in block synchronization. In this paper, we propose two new methods to construct the QSCs from the Euclidean sums of cyclic or constacyclic codes over finite rings. The first one is derived from the Calderbank–Shor–Steane (CSS) construction applied to Euclidean sums of cyclic codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the Euclidean sums of constacyclic codes over semi-local rings \({\mathbb {F}}_{p}+v{\mathbb {F}}_{p}\) with \(v^2=v\). By using the two methods, concrete examples are presented to construct new QSCs, whose synchronization capabilities attain the upper bound.

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Acknowledgements

X. Liu was supported by Research Funds of Hubei Province (Grant No. Q20174503).

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Authors and Affiliations

  1. School of Science, Hubei Polytechnic University, Huangshi, 435003, Hubei, China

    Yanqing Dai

  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. Yanqing Dai
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  2. Xiusheng Liu
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Dai, Y., Liu, X. QSCs from the Euclidean sums of cyclic codes over finite rings. Quantum Inf Process 21, 295 (2022). https://doi.org/10.1007/s11128-022-03625-3

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