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New Entanglement-Assisted Quantum MDS Codes Derived From Generalized Reed-Solomon Codes

  • Guanmin Guo
  • Ruihu LiEmail author
Article

Abstract

Entanglement-assisted quantum error-correcting codes (abbreviate to EAQECCs) expand the usual paradigm of quantum error correction by allowing two parties to make use of pre-shared entanglement. It is well-known that we can construct an EAQECC from arbitrary classical linear code. In this paper, we construct several classes of entanglement-assisted quantum MDS (EAQMDS) codes by utilizing generalized Reed-Solomon (GRS) codes. The main contribution of the paper is extend the code length of EAQMDS in the literature (Guo et al. 2019). Consequently, the results show that almost all of these EAQMDS codes are new in the sense that the parameters of these codes are not covered by the previously known ones.

Keywords

Entanglement-assisted quantum error-correcting codes Generalized Reed-Solomon codes MDS codes Rank 

Mathematics Subject Classification (2010)

81P45 81P70 94B05 

Notes

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant Nos. 11801564 and 11471011.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Basic SciencesAir Force Engineering UniversityXi’anPeople’s Republic of China

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