Skip to main content
SpringerLink
Log in

New EAQMDS codes constructed from negacyclic codes

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we construct four families of entanglement-assisted quantum error-correcting codes (EAQECCs) with flexible parameters from negacyclic codes. By selecting different defining sets, our codes are new in the sense that their parameters are not covered by the codes available in the literature. Moreover, the EAQECCs we constructed are optimal and have larger minimum distance compared with the known codes with the same length.

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. Shor, P.: Scheme for reducing decoherence in quantum memory. Phys. Rev. A 52(4), 2493–2496 (1995)

    Article  ADS  Google Scholar 

  2. Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. La Guardia, G.G., Palazzo, J.R.: Constructions of new families of nonbinary CSS codes. Discret. Math. 310, 2935–2945 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Diao, L., Gao, J., Lu, J.: On \(Z_pZ_p[v]\) additive cyclic codes. Adv. Math. Commun. 14(4), 555–572 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gao, J., Wang, Y.: Quantum codes derived from negacyclic codes. Int. J. Theor. Phys. 57(3), 682–686 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gao, J., Wang, Y.: \(u\)-Constacyclic codes over \(F_p+uF_p\) and their applications of constructing new non-binary quantum codes. Quantum Inf. Process. 17(1), 1–9 (2018)

    Article  ADS  Google Scholar 

  8. Ezerman, M.F., Ling, S., Solé, P.: Additive asymmetric quantum codes. IEEE Trans. Inf. Theory 57, 5536–5550 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. La Guardia, G.G.: Asymmetric quantum convolutional codes. Quantum Inf. Process. 15(1), 167–183 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Chen, J., Chen, Y., Huang, Y., Feng, C.: New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes. Quantum Inf. Process. 18(2), 1–29 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  11. Brun, T., Devetak, I., Hsieh, M.: Correcting quantum errors with entanglement. Science 314(5798), 436–439 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Grassl, M.: Entanglement-Assisted Quantum Communication Beating the Quantum Singleton Bound. AQIS, Taiwan (2016)

    Google Scholar 

  13. Lai, C., Ashikhmin, A.: Linear programming bounds for entanglement-assisted quantum error-correcting codes by split weight enumerators. IEEE Trans. Inf. Theory 64(1), 622–639 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wilde, M., Brun, T.: Optimal entanglement formulas for entanglement-assisted quantum coding. Phys. Rev. A 77(6), 064302 (2008)

    Article  ADS  Google Scholar 

  15. Guo, L., Li, R.: Linear Plotkin bound for entanglement-assisted quantum codes. Phys. Rev. A 87, 032309 (2013)

    Article  ADS  Google Scholar 

  16. Hsieh, M., Devetak, I., Brun, T.: General entanglement-assisted quantum error-correcting codes. Phys. Rev. A 76, 064302 (2007)

    Article  Google Scholar 

  17. Li, R., Xu, G., Lü, 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 

  18. Lü, L., Li, R.: Entanglement-assisted quantum codes constructed from primitive quaternary BCH codes. Int. J. Quantum Inf. 12(3), 1450015 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Chen, J., Huang, Y., Feng, C., Chen, R.: Entanglement-assisted quantum MDS codes constructed from negacyclic codes. Quantum Inf. Process. 16(12), 1–22 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  20. Chen, X., Zhu, S., Kai, X.: Entanglement-assisted quantum MDS codes constructed from constacyclic codes. Quantum Inf. Process. 17(273), 1–18 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  21. Qian, J., Zhang, L.: On MDS linear complementary dual codes and entanglement-assisted quantum codes. Des. Codes Cryptogr. 86(7), 1565–1572 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lü, 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  MATH  Google Scholar 

  23. Luo, G., Cao, X.: Two new families of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes. Quantum Inf. Process. 18(89), 1–12 (2019)

    MathSciNet  MATH  Google Scholar 

  24. Liu, X., Yu, L., Hu, P.: New entanglement-assisted quantum codes from \(k\)-Galois dual codes. Finite Fields Their Appl. 55, 21–32 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  25. Qian, J., Zhang, L.: Constructions of new entanglement-assisted quantum MDS and almost MDS codes. Quantum Inf. Process. 18(71), 1–12 (2019)

    MathSciNet  MATH  Google Scholar 

  26. Wang, J., Li, R., Lv, J., Guo, G., Liu, Y.: Entanglement-assisted quantum error correction codes with length \(n = q^2 + 1\). Quantum Inf. Process. 18(292), 1–21 (2019)

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  28. 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  MATH  Google Scholar 

  29. Krishna, A., Sarwate, D.V.: Pseudocyclic maximum-distance-separable codes. IEEE Trans. Inf. Theory 36(4), 880–884 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kai, X., Zhu, S.: New quantum MDS codes from negacyclic codes. IEEE Trans. Inf. Theory 59(2), 1193–1197 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  31. Koroglu, M.E.: New entanglement-assisted MDS quantum codes from constacyclic codes. Quantum Inf. Process. 18(44), 1–28 (2019)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

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

    Wan Jiang & Shixin Zhu

  2. Intelligent Interconnected Systems Laboratory of Anhui Province (Hefei University of Technology), Hefei, People’s Republic of China

    Wan Jiang & Shixin Zhu

  3. School of Internet, Anhui University, Hefei, 230039, Anhui, People’s Republic of China

    Xiaojing Chen

Authors
  1. Wan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shixin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaojing Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaojing Chen.

Additional information

Publisher's Note

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

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, W., Zhu, S. & Chen, X. New EAQMDS codes constructed from negacyclic codes. Quantum Inf Process 19, 424 (2020). https://doi.org/10.1007/s11128-020-02934-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02934-9

Keywords

Search

Navigation