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Quantum MDS codes with large minimum distance

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Abstract

Quantum MDS codes are an important family of quantum codes. In this paper, using generalized Reed–Solomon codes and Hermitian construction, we construct seven classes of quantum MDS codes. All of them provide large minimum distance and most of them are new in the sense that the parameters of quantum codes are different from all the previously known ones.

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Acknowledgments

The authors express their gratitude to the anonymous reviewers for their detailed and constructive comments which are very helpful to the improvement of the presentation of this paper. Research supported by the National Natural Science Foundation of China under Grant Nos. 11431003 and 61571310.

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Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Tao Zhang & Gennian Ge

  2. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, Zhejiang, China

    Tao Zhang

  3. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048, China

    Gennian Ge

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  1. Tao Zhang
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  2. Gennian Ge
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Correspondence to Gennian Ge.

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Communicated by D. Jungnickel.

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Zhang, T., Ge, G. Quantum MDS codes with large minimum distance. Des. Codes Cryptogr. 83, 503–517 (2017). https://doi.org/10.1007/s10623-016-0245-0

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  • DOI: https://doi.org/10.1007/s10623-016-0245-0

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