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New quantum MDS codes over finite fields

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Abstract

In this paper, we present three new classes of q-ary quantum MDS codes utilizing generalized Reed–Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some q-ary quantum MDS codes can be bigger than \(\frac{q}{2}+1\). Comparing to previous known constructions, the lengths of codes in our constructions are more flexible.

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Acknowledgements

This research is supported by National Natural Science Foundation of China under Grant Nos. 11471008 and 11871025 and the self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (Grant No. CCNU18TS028).

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Authors and Affiliations

  1. School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, China

    Xiaolei Fang & Jinquan Luo

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  1. Xiaolei Fang
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  2. Jinquan Luo
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Correspondence to Jinquan Luo.

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Fang, X., Luo, J. New quantum MDS codes over finite fields. Quantum Inf Process 19, 16 (2020). https://doi.org/10.1007/s11128-019-2506-0

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