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Cryptography and Communications

, Volume 10, Issue 6, pp 1165–1182 | Cite as

Some quantum MDS codes with large minimum distance from generalized Reed-Solomon codes

  • Xueying Shi
  • Qin YueEmail author
  • Yaotsu Chang
Article

Abstract

Quantum maximum-distance-separable (MDS) codes are a significant class of quantum codes. In this paper, we mainly utilize classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct five new classes of quantum MDS codes with large minimum distance.

Keywords

Quantum MDS codes Hermitian self-orthogonal Generalized Reed-Solomon codes 

Mathematics Subject Classification (2010)

81P70 

Notes

Acknowledgments

This research is supported by National Natural Science Foundation of China (No. 61772015) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17-0225). The paper is also supported by Ministry of Science and Technology, Taiwan, under Grant MOST104-2115-M-214-002-MY2. Additionally, the authors are grateful to the Editor and the anonymous referees for their useful comments and suggestions which helped to improve the presentation of this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China
  2. 2.State Key Laboratory of CryptologyBeijingPeople’s Republic of China
  3. 3.Department of Financial and Computational MathematicsI-SHOU UniversityKaohsiung CityRepublic of China

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