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Four classes of new entanglement-assisted quantum optimal codes

Journal of Applied Mathematics and Computing volume 67, pages 937–952 (2021)Cite this article

Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) provide a general framework for quantum code construction, which overcome certain self-orthogonal restriction. It becomes one main task in quantum error-correction to find EAQECCs with good parameters, especially entanglement-assisted quantum maximum distance separable (EAQMDS) codes. In this work, we construct four new families of EAQECC codes with flexible parameters in view of negacyclic codes. It is worth pointing out that those EAQECCs are EAQMDS codes when \(d\le (n+2)/2\). By exploring the selection of defining sets, the constructed EAQECCs possess larger minimum distance in contrast with the known results in the literatures.

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Acknowledgements

The authors would like to thank the referees and editor in chief for their helpful comments and a very meticulous reading of this manuscript.

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Authors and Affiliations

  1. School of Internet, Anhui University, Hefei, 230601, Anhui, People’s Republic of China

    Xiaojing Chen

  2. School of Mathematics, Hefei University of Technology, Hefei, 230601, Anhui, People’s Republic of China

    Shixin Zhu & Wan Jiang

  3. School of Artificial Intelligence and Big Data, Hefei University, Hefei, 230601, Anhui, People’s Republic of China

    Binbin Pang

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  1. Xiaojing Chen
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  2. Shixin Zhu
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  3. Wan Jiang
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  4. Binbin Pang
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Correspondence to Xiaojing Chen.

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This research is supported by the National Natural Science Foundation of China (Nos. 12001002, 61772168, 61972126) and the Natural Science Foundation of Anhui Province (No. 2008085QA04).

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Chen, X., Zhu, S., Jiang, W. et al. Four classes of new entanglement-assisted quantum optimal codes. J. Appl. Math. Comput. 67, 937–952 (2021). https://doi.org/10.1007/s12190-021-01523-y

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  • DOI: https://doi.org/10.1007/s12190-021-01523-y

Keywords

  • EAQECCs
  • EAQMDS codes
  • Negacyclic codes
  • Defining sets