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New EAQEC codes from cyclic codes over \(\mathbb {F}_{q}+u\mathbb {F}_{q}\)

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Abstract

In this paper, we provide two methods of constructing entanglement-assisted quantum error-correcting (EAQEC, for short) codes from cyclic codes over finite chain rings \(\mathbb {F}_{q}+u\mathbb {F}_{q}\), where \(q=p^m\), p is a prime number and \(m\ge 1\) is an integer. The first one is derived from the Euclidean hulls applied to the cyclic codes over finite chain rings \(\mathbb {F}_{q}+u\mathbb {F}_{q}\). The second construction is derived from the Hermitian hulls applied to the cyclic codes over finite chain rings \(\mathbb {F}_{q^{2}}+u\mathbb {F}_{q^{2}}\). Moreover, most of the EAQEC codes constructed are new in the sense that their parameters are different from all the previously known ones.

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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.

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

    Hualu Liu

  2. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, Hubei, China

    Xiusheng Liu

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  1. Hualu Liu
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Liu, H., Liu, X. New EAQEC codes from cyclic codes over \(\mathbb {F}_{q}+u\mathbb {F}_{q}\). Quantum Inf Process 19, 85 (2020). https://doi.org/10.1007/s11128-020-2580-3

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