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On the Constructions of Quantum MDS Convolutional Codes

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Abstract

Quantum convolutional codes, which are the correct generalization to quantum domain of their classical analogs, were introduced to overcome decoherence during long distance quantum communications. In this paper, we construct some classes of quantum convolutional codes via classical constacyclic codes. These codes are maximum-distance-separable (MDS) codes in the sense that they achieve the Singleton bound for pure convolutional stabilizer codes. Furthermore, compared with some of the codes available in the literature, our codes have better parameters and are more general.

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Acknowledgements

We are grateful to the anonymous referees and the associate editor for useful comments and suggestions that improved the presentation and quality of this paper.

Funding

The work was supported by the National Natural Science Foundation of China (12271137, U21A20428, 12171134).

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230601, Anhui, China

    Sujuan Huang & Shixin Zhu

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  1. Sujuan Huang
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  2. Shixin Zhu
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All authors contributed to the study conception and design. The first draft of the manuscript was written by Sujuan Huang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Sujuan Huang.

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Huang, S., Zhu, S. On the Constructions of Quantum MDS Convolutional Codes. Int J Theor Phys 62, 108 (2023). https://doi.org/10.1007/s10773-023-05366-0

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