Abstract
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank–Shor–Steane (CSS) construction applied to self-dual codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the linear codes over finite chain ring \({\mathbb {F}}_{p^{2m}}+u{\mathbb {F}}_{p^{2m}}\). The good parameters of quantum codes from cyclic codes over finite chain rings are obtained.
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Acknowledgements
The authors would like to sincerely thank the editor and the anonymous referees for a very meticulous reading of this manuscript and for valuable suggestions which help to create an improved version. This work was supported by Research Funds of Hubei Province, Grant No. D20144401, the Educational Commission of Hubei Province, Grant No. B2015096, and Research Project of Hubei Polytechnic University, Grant No. 17xjzo3A.
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Liu, X., Liu, H. Quantum codes from linear codes over finite chain rings. Quantum Inf Process 16, 240 (2017). https://doi.org/10.1007/s11128-017-1695-7
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DOI: https://doi.org/10.1007/s11128-017-1695-7