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Quantum MDS codes from BCH constacyclic codes

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Abstract

One central theme in quantum error correction is to construct quantum codes that have large minimum distances. It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. Recently, some quantum MDS codes have been constructed from constacyclic codes. Under these constructions, one of the most important problems is to ensure these constacyclic codes are Hermitian dual-containing. This paper presents a method for determining the maximal designed distance of \([[n, k, d]]_q\) quantum MDS codes from constacyclic codes with fixed n and q. From the method, we can get not only those known quantum MDS codes from constacyclic codes but also a new class of quantum MDS code from Hermitian dual-containing MDS constacyclic code.

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Authors and Affiliations

  1. School of Cyberspace, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    Liqin Hu

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Qin Yue

  3. Dongguan University of Technology, Guangdong, 523808, People’s Republic of China

    Xianmang He

Authors
  1. Liqin Hu
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  2. Qin Yue
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  3. Xianmang He
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Corresponding author

Correspondence to Liqin Hu.

Additional information

The paper is partly supported by NNSF of China (Nos. 61602144, 61772015).

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Hu, L., Yue, Q. & He, X. Quantum MDS codes from BCH constacyclic codes . Quantum Inf Process 17, 323 (2018). https://doi.org/10.1007/s11128-018-2049-9

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  • DOI: https://doi.org/10.1007/s11128-018-2049-9

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