Entanglement-assisted quantum MDS codes constructed from constacyclic codes

03/01/2018
by   Xiaojing Chen, et al.
Hefei University of Technology
0

Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed three classes of new EAQECCs which satisfy the entanglement-assisted quantum Singleton bound. Besides, three classes of EAQECCs with maximal entanglement from constacyclic codes are constructed in the meanwhile.

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References

  • [1] Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A , 2493-2496 (1995)
  • [2] Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. , 793-797 (1996)
  • [3] Steane, A. M.: Simple quantum error-correcting codes. Phys. Rev. A , 4741-4751 (1996)
  • [4] 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 , 1369-1387 (1998)
  • [5] Grassl, M., Beth, T.: On optimal quantum codes. Int. J. Quantum Inf. , 55-64 (2004)
  • [6] Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary quantum stabilizer codes over finite fields. IEEE Trans. Inf. Theory , 4892-4914 (2006)
  • [7] La Guardia, G. G.: Constructions of new families of nonbinary quantum codes. Phys. Rev. A , 042331(1-11) (2009)
  • [8] Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory , 1183-1188 (2007)
  • [9] Brun, T., Devetak, I., Hsieh, M.-H.: Correcting quantum errors with entanglement. Science , 436-439 (2006)
  • [10] Wilde, M., Brun, T.: Optimal entanglement formulas for entanglement-assisted quantum coding. Phys. Rev. A , 064302 (2008)
  • [11] Lai, C., Brun, T.: Entanglement increases the error-correcting ability of quantum error-correcting codes. Phys. Rev. A , 012320 (2013)
  • [12] Lu, L., Li, R., Guo, L., Fu, Q.: Maximal entanglement entanglement-assisted quantum codes constructed from linear codes. Quantum Inf. Process. (1), 165-182 (2015)
  • [13] Brun, T., Devetak, I., Hsieh, M.-H.: Catalytic quantum error correction. IEEE Trans. Inf. Theory , 3073-3089 (2014)
  • [14] Grassl, M.: Entanglement-assisted quantum communication beating the quantum singleton bound. AQIS, Taiwan (2016)
  • [15] Qian, J., Zhang, L.: On MDS linear complementary dual codes and entanglement-assisted quantum codes. Des. Codes Cryptogr. (2017). https://doi.org/10.1007/s10623-017-0413-x
  • [16] Guenda, K., Jitman, S., Gulliver, T. A. : Constructions of good entanglement-assisted quanutm error cottecting codes. Des. Codes Cryptogr. (2018) 86: 121. https://doi.org/10.1007/s10623-017-0330-z
  • [17]

    Li, R., Zuo, F., Liu, Y.: A study of skew asymmetric

    -cyclotomic coset and its application. J. Air Force Eng. Univ.(Nat. Sci. Ed.) (1), 87-89 (2011).(in Chinese)
  • [18] L, L., Li, R.: Entanglement-assisted quantum codes constructed from primitive quaternary BCH codes. Int. J. Quantum Inf. (03), 1450015(1-14) (2014)
  • [19] Chen, J., Huang, Y., Feng, C., Chen, R.: Entanglement-assisted quantum MDS codes constructed from negacyclic codes. Quantum Inf. Process. , 303(1-22) (2017)
  • [20] Lu, L., Li, R., Guo, L., Ma, Y., Liu Y: Entanglement-assisted quantum MDS codes from negacyclic codes. Quantum Inf. Process. (2018) 17: 69. https://doi.org/10.1007/s11128-018-1838-5
  • [21] Kai, X., Zhu, S., Li, P.: Constacyclic Codes and Some New Quantum MDS Codes. IEEE Trans. Inf. Theory , 2080-2086 (2014)
  • [22] Chen, X., Zhu, S., Kai, X.: Two classes of new optimal asymmetric quantum codes. Int. J. Theor. Phys. (2018). https://doi.org/10.1007/s10773-018-3708-4
  • [23] Aydin, N., Siap, I., Ray-Chaudhuri, D.K.: The Structure of -Generator Quasi-Twisted Codes and New Linear Codes. Des. Codes Cryptogr. , 313-326 (2001)
  • [24] Krishna, A., Sarwate, D.V.: Pseudocyclic maximum-distance-separable codes. IEEE Trans. Inf. Theory , 2080-2086 (2014)
  • [25] Macwilliams, F.J., Sloane, N.J.A.: The theory of Error-Correcting Codes. North-Holland, Amsterdam, The Netherlands, 1997.
  • [26] Krishna, A., Sarwate, D. V.: Pseudocyclic maximum-distance-separable codes. IEEE Trans. Inf. Theory , 2080-2086 (2014)