Skip to main content
SpringerLink
Log in

New classes of entanglement-assisted quantum MDS codes

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, two new classes of entanglement-assisted quantum MDS codes (EAQMDS codes for short) with length n being a factor of \(q^2\pm 1\) are presented via cyclic codes over finite fields of odd characteristic. Among our constructions, there are several EAQMDS codes with new parameters which have never been reported. Moreover, some of them have much larger minimum distance than known results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ashikhmin, A., Litsyn, S., Tsfasman, M.: Asymptotically good quantum codes. Phys. Rev. A 63, 032311 (2001)

    Article  ADS  Google Scholar 

  2. Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098 (1996)

    Article  ADS  Google Scholar 

  3. Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory 44, 1369–1387 (1998)

    Article  MathSciNet  Google Scholar 

  4. Chen, H.: Some good quantum error-correcting codes from algebraic-geometric codes. IEEE Trans. Inf. Theory 47, 2059–2061 (2001)

    Article  MathSciNet  Google Scholar 

  5. Chen, J., Huang, Y., Feng, C., Chen, R.: Entanglement-assisted quantum MDS codes constructed from negacyclic codes. Quantum Inf. Process. 16, 303 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  6. Chen, X., Zhu, S., Kai, X.: Entanglement-assisted quantum MDS codes constructed from constacyclic codes. Quantum Inf. Process. 17, 273 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  7. Fan, J., Chen, H., Xu, J.: Constructions of \(q\)-ary entanglement-assisted quantum MDS codes with minimum distance greater than \(q+1\). Quantum Inf. Comput. 16, 0423–0434 (2016)

    MathSciNet  Google Scholar 

  8. Fujiwara, Y., Clark, D., Vandendriessche, P., Boeck, M.D., Tonchev, V.D.: Entanglement-assisted quantum low-density parity-check codes. Phys. Rev. A 82, 042338 (2010)

    Article  ADS  Google Scholar 

  9. Guenda, K., Jitman, S., Gulliver, T.A.: Constructions of good entanglement-assisted quantum error correcting codes. Des. Codes Cryptogr. 86, 121–136 (2018)

    Article  MathSciNet  Google Scholar 

  10. Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  11. Hsieh, M.H., Yen, W.T., Hsu, L.Y.: High performance entanglement-assisted quantum LDPC codes need little entanglement. IEEE Trans. Inf. Theory 57, 1761–1769 (2011)

    Article  MathSciNet  Google Scholar 

  12. Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52, 4892–4914 (2006)

    Article  MathSciNet  Google Scholar 

  13. Koroglu, M.E.: New entanglement-assisted MDS quantum codes from constacyclic codes. Quantum Inf. Process. 18, 44 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  14. Lai, C.Y., Brun, T.A., Wilde, M.M.: Duality in entanglement-assisted quantum error correction. IEEE Trans. Inf. Theory 59, 4020–4024 (2013)

    Article  MathSciNet  Google Scholar 

  15. Li, R., Xu, G., Lu, L.: Decomposition of defining sets of BCH codes and its applications. J. Air Force Eng. Univ. (Nat. Sci. Ed.) 14(2), 86–89 (2013). (in Chinese)

    Google Scholar 

  16. Li, X.: Quantum cyclic and constacyclic codes. IEEE Trans. Inf. Theory 50, 547–549 (2004)

    Article  MathSciNet  Google Scholar 

  17. Lu, L., Li, R., Guo, L., Ma, Y., Liu, Y.: Entanglement-assisted quantum MDS codes from negacyclic codes. Quantum Inf. Process. 17, 69 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  18. Lu, L., Li, R., Ma, W., Li, R., Ma, Y., Liu, Y., Cao, H.: Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance. arXiv:1803.04168

  19. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  20. Qian, J., Zhang, L.: Nonbinary quantum codes derived from group character codes. Int. J. Quantum Inf. Process. 10, 1250042 (2012)

    Article  MathSciNet  Google Scholar 

  21. Qian, J., Zhang, L.: New optimal subsystem codes. Discrete Math. 313, 2451–2455 (2013)

    Article  MathSciNet  Google Scholar 

  22. Qian, J., Zhang, L.: On MDS linear complementary dual codes and entanglement-assisted quantum codes. Des. Codes Cryptogr. 86, 1565–1572 (2017)

    Article  MathSciNet  Google Scholar 

  23. Qian, J., Zhang, L.: Constructions of new entanglement-assisted quantum MDS and almost MDS codes. Quantum Inf. Process. 18, 71 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  24. Steane, A.M.: Simple quantum error-correcting codes. Phys. Rev. A 54, 4741 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  25. Wang, J., Li, R., Lv, J., Song, H.: Entanglement-assisted quantum codes from cyclic codes and negacyclic codes. Quantum Inf. Process. 19, 5 (2020)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Funding

Funding was provided by National Science Fundation of China (Grant No. 11471008) and Self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (Grant No. CCNU18TS028).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, China

    Renjie Jin, Derong Xie & Jinquan Luo

Authors
  1. Renjie Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Derong Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jinquan Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinquan Luo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, R., Xie, D. & Luo, J. New classes of entanglement-assisted quantum MDS codes. Quantum Inf Process 19, 289 (2020). https://doi.org/10.1007/s11128-020-02771-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02771-w

Keywords

Search

Navigation