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The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p

Year 2019, Volume: 7 Issue: 1, 87 - 93, 30.04.2019
https://doi.org/10.36753/mathenot.559260

Abstract


References

  • [1] Dertli, A., Cengellenmis, Y. and Eren, S., Quantum codes over F2 + uF2 + vF2. Palestine Journal of Math. (2015), 1-6.
  • [2] Dertli, A., Cengellenmis, Y. and Eren, S., Some results on the linear codes over the finite ring F2+v1F2+:::+vrF2. International Journal of Quantum Information 14(2016), 1650012.
  • [3] Dertli, A., Cengellenmis, Y. and Eren, S., On quantum codes obtained from cyclic codes over A2. Int. J. Quantum Inform. 13 (2015), 1550031.
  • [4] Dertli, A., Cengellenmis, Y. and Eren, S., Quantum codes over the ring F2 +uF2 +u2F2 +:::+umF2. Int. Journal of Alg. 9(2015), 115 - 121.
  • [5] Calderbank, A.R., Rains, E.M., Shor, P.M. and Sloane, N.J.A., Quantum error correction via codes over GF (4). IEEE Trans. Inf. Theory 44( 1998), 1369-1387.
  • [6] Melakheso, A. and Guenda, K., The dual and the Gray image of codes over Fq +vFq +v2Fq, arXiv:1504.08097v1.
  • [7] Seroussi, G. and Lempel, A., Factorization of Symmetric Matrices and Trace-Orthogonal Bases in Finite Fields, SIAM. Journal Comput. 9(1980), 758-767.
  • [8] Gao, J., Quantum codes from cyclic codes over Fq +vFq +v2Fq +v3Fq. Int. Journal of Quantum Information, 2015.
  • [9] Qian, J., Quantum codes from cyclic codes over F2 + vF2. Journal of Inform.& computational Science 10( 2013), 1715-1722.
  • [10] Qian, J., Ma, W. and Gou, W., Quantum codes from cyclic codes over finite ring. Int. J. Quantum Inform. 7( 2009), 1277-1283.
  • [11] Qian, J., Ma,W. and X.Wang, Quantum error correcting codes from quasi-cyclic codes over finite ring. Int. J. Quantum Inform. 6( 2008), 1263-1269.
  • [12] Shi, M. and Yao, T., Skew cyclic codes over Fq + vFq + v2Fq + ::: + vm􀀀1Fq, 2016.
  • [13] Sari, M and Siap, I., On Quantum codes from cyclic codes over a class of non chain rings. Bull Korean Math. Soc. 53(2016), 617-1628.
  • [14] Ashraf, M. and Mohammad, G., Quantum codes from cyclic codes over F3 + vF3. International Journal of Quantum Information 12(2014), 1450042.
  • [15] Ashraf, M. and Mohammad, G., Construction of quantum codes from cyclic codes over Fp + vFp. International Journal of Information and Coding Theory 2(2015), 137-144.
  • [16] Ashraf, M. and Mohammad, G., Quantum codes from cyclic codes over Fq + uFq + vFq + uvFq. Quantum Information Processing 10(2016), 4089-4098.
  • [17] Kai, X. and Zhu, S., Quaternary construction of quantum codes from cyclic codes over F4 +uF4. Int. J. Quantum Inform. 9( 2011), 689-700.
  • [18] Yin, X. and Ma,W., Gray Map and Quantum Codes Over The Ring F2+uF2+u2F2. International Joint Conferences of IEEE TrustCom-11, 2011.
Year 2019, Volume: 7 Issue: 1, 87 - 93, 30.04.2019
https://doi.org/10.36753/mathenot.559260

Abstract

References

  • [1] Dertli, A., Cengellenmis, Y. and Eren, S., Quantum codes over F2 + uF2 + vF2. Palestine Journal of Math. (2015), 1-6.
  • [2] Dertli, A., Cengellenmis, Y. and Eren, S., Some results on the linear codes over the finite ring F2+v1F2+:::+vrF2. International Journal of Quantum Information 14(2016), 1650012.
  • [3] Dertli, A., Cengellenmis, Y. and Eren, S., On quantum codes obtained from cyclic codes over A2. Int. J. Quantum Inform. 13 (2015), 1550031.
  • [4] Dertli, A., Cengellenmis, Y. and Eren, S., Quantum codes over the ring F2 +uF2 +u2F2 +:::+umF2. Int. Journal of Alg. 9(2015), 115 - 121.
  • [5] Calderbank, A.R., Rains, E.M., Shor, P.M. and Sloane, N.J.A., Quantum error correction via codes over GF (4). IEEE Trans. Inf. Theory 44( 1998), 1369-1387.
  • [6] Melakheso, A. and Guenda, K., The dual and the Gray image of codes over Fq +vFq +v2Fq, arXiv:1504.08097v1.
  • [7] Seroussi, G. and Lempel, A., Factorization of Symmetric Matrices and Trace-Orthogonal Bases in Finite Fields, SIAM. Journal Comput. 9(1980), 758-767.
  • [8] Gao, J., Quantum codes from cyclic codes over Fq +vFq +v2Fq +v3Fq. Int. Journal of Quantum Information, 2015.
  • [9] Qian, J., Quantum codes from cyclic codes over F2 + vF2. Journal of Inform.& computational Science 10( 2013), 1715-1722.
  • [10] Qian, J., Ma, W. and Gou, W., Quantum codes from cyclic codes over finite ring. Int. J. Quantum Inform. 7( 2009), 1277-1283.
  • [11] Qian, J., Ma,W. and X.Wang, Quantum error correcting codes from quasi-cyclic codes over finite ring. Int. J. Quantum Inform. 6( 2008), 1263-1269.
  • [12] Shi, M. and Yao, T., Skew cyclic codes over Fq + vFq + v2Fq + ::: + vm􀀀1Fq, 2016.
  • [13] Sari, M and Siap, I., On Quantum codes from cyclic codes over a class of non chain rings. Bull Korean Math. Soc. 53(2016), 617-1628.
  • [14] Ashraf, M. and Mohammad, G., Quantum codes from cyclic codes over F3 + vF3. International Journal of Quantum Information 12(2014), 1450042.
  • [15] Ashraf, M. and Mohammad, G., Construction of quantum codes from cyclic codes over Fp + vFp. International Journal of Information and Coding Theory 2(2015), 137-144.
  • [16] Ashraf, M. and Mohammad, G., Quantum codes from cyclic codes over Fq + uFq + vFq + uvFq. Quantum Information Processing 10(2016), 4089-4098.
  • [17] Kai, X. and Zhu, S., Quaternary construction of quantum codes from cyclic codes over F4 +uF4. Int. J. Quantum Inform. 9( 2011), 689-700.
  • [18] Yin, X. and Ma,W., Gray Map and Quantum Codes Over The Ring F2+uF2+u2F2. International Joint Conferences of IEEE TrustCom-11, 2011.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Yasemin Cengellenmis This is me

Abdullah Dertli

Publication Date April 30, 2019
Submission Date November 6, 2017
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Cengellenmis, Y., & Dertli, A. (2019). The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p. Mathematical Sciences and Applications E-Notes, 7(1), 87-93. https://doi.org/10.36753/mathenot.559260
AMA Cengellenmis Y, Dertli A. The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p. Math. Sci. Appl. E-Notes. April 2019;7(1):87-93. doi:10.36753/mathenot.559260
Chicago Cengellenmis, Yasemin, and Abdullah Dertli. “The Quantum Codes over F_q and Quantum Quasi-Cyclic Codes over F_p”. Mathematical Sciences and Applications E-Notes 7, no. 1 (April 2019): 87-93. https://doi.org/10.36753/mathenot.559260.
EndNote Cengellenmis Y, Dertli A (April 1, 2019) The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p. Mathematical Sciences and Applications E-Notes 7 1 87–93.
IEEE Y. Cengellenmis and A. Dertli, “The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 87–93, 2019, doi: 10.36753/mathenot.559260.
ISNAD Cengellenmis, Yasemin - Dertli, Abdullah. “The Quantum Codes over F_q and Quantum Quasi-Cyclic Codes over F_p”. Mathematical Sciences and Applications E-Notes 7/1 (April 2019), 87-93. https://doi.org/10.36753/mathenot.559260.
JAMA Cengellenmis Y, Dertli A. The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p. Math. Sci. Appl. E-Notes. 2019;7:87–93.
MLA Cengellenmis, Yasemin and Abdullah Dertli. “The Quantum Codes over F_q and Quantum Quasi-Cyclic Codes over F_p”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, 2019, pp. 87-93, doi:10.36753/mathenot.559260.
Vancouver Cengellenmis Y, Dertli A. The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p. Math. Sci. Appl. E-Notes. 2019;7(1):87-93.

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