[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

New entanglement-assisted MDS quantum codes from constacyclic codes

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new classes of entanglement-assisted quantum maximum-distance-separable codes.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

    Article  ADS  Google Scholar 

  2. Aydin, N., Siap, I., Ray-Chaudhuri, D.K.: The structure of 1-generator quasi-twisted codes and new linear codes. Des. Codes Cryptogr. 24, 313–326 (2001)

    Article  MathSciNet  Google Scholar 

  3. Brun, T., Devetak, I., Hsieh, M.H.: Correcting quantum errors with entanglement. Science 52, 436 (2006)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. 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 

  6. Chen, B., Ling, S., Zhang, G.: Application of constacyclic codes to quantum MDS codes. IEEE Trans. Inf. Theory 61, 1474–1484 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. 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 

  9. 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 

  10. 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 

  11. Grassl, M.: Entanglement-assisted quantum communication beating the quantum singleton bound. In: AQIS, Taiwan (2016)

  12. 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 

  13. Hsieh, M.H., Devetak, I., Brun, T.A.: General entanglement-assisted quantum error-correcting codes. Phys. Rev. A 76, 062313 (2007)

    Article  ADS  Google Scholar 

  14. 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 

  15. Kai, X., Zhu, S.: New quantum MDS codes from negacyclic codes. IEEE Trans. Inf. Theory 59, 1193–1197 (2013)

    Article  MathSciNet  Google Scholar 

  16. Kai, X., Zhu, S., Li, P.: Constacyclic codes and some new quantum MDS codes. IEEE Trans. Inf. Theory 60, 2080–2086 (2014)

    Article  MathSciNet  Google Scholar 

  17. 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 

  18. Krishna, A., Sarwate, D.V.: Pseudocyclic maximum-distance-separable codes. IEEE Trans. Inf. Theory 36, 880–884 (1990)

    Article  MathSciNet  Google Scholar 

  19. La Guardia, G.G.: On optimal constacyclic codes. Linear Algebra Appl. 496, 594–610 (2016)

    Article  MathSciNet  Google Scholar 

  20. 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 

  21. Li, R., Li, X., Guo, L.: On entanglement-assisted quantum codes achieving the entanglement-assisted Griesmer bound. Quantum Inf. Process. 14, 4427–4447 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  22. Li, S., Xiong, M., Ge, G.: Pseudo-cyclic codes and the construction of quantum MDS codes. IEEE Trans. Inf. Theory 62, 1703–1710 (2016)

    Article  MathSciNet  Google Scholar 

  23. Lu, L., Li, R.: Entanglement-assisted quantum codes constructed from primitive quaternary BCH codes. Int. J. Quantum Inf. 12, 1450015 (2014)

    Article  MathSciNet  Google Scholar 

  24. 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 

  25. Lu, L., Ma, W., Li, R., Ma, Y., Liu, Y., Cao, H.: Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance. Finite Fields Their Appl. 53, 309–325 (2018)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  29. 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 

  30. Shor, P.W.: Scheme for reducing decoherence in quantum memory. Phys. Rev. A 52, 2493–2496 (1995)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  32. Wilde, M.M., Brun, T.A.: Optimal entanglement formulas for entanglement-assisted quantum coding. Phys. Rev. A 77, 064302 (2008)

    Article  ADS  Google Scholar 

  33. Xiaoyan, L.: Quantum cyclic and constacyclic codes. IEEE Trans. Inf. Theory 50, 547–549 (2004)

    Article  MathSciNet  Google Scholar 

  34. Zhang, T., Ge, G.: Some new classes of quantum MDS codes from constacyclic codes. IEEE Trans. Inf. Theory 61, 5224–5228 (2015)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author is very grateful to the reviewers for their comments and suggestions that improved the presentation and quality of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mehmet E. Koroglu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koroglu, M.E. New entanglement-assisted MDS quantum codes from constacyclic codes. Quantum Inf Process 18, 44 (2019). https://doi.org/10.1007/s11128-018-2155-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-2155-8

Keywords

Mathematics Subject Classification

Navigation