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

Yasemin Cengellenmis; Abdullah Dertli

doi:10.36753/mathenot.559260

EN

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

Abstract

Keywords

Cyclic codes,Quasi-cyclic codes,Quantum codes

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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Yasemin Cengellenmis This is me

Abdullah Dertli

Publication Date

April 30, 2019

Submission Date

November 6, 2017

Acceptance Date

-

Published in Issue

Year 2019 Volume: 7 Number: 1

DOI

https://doi.org/10.36753/mathenot.559260

IZ

https://izlik.org/JA22WN79TM

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

1.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. doi:10.36753/mathenot.559260

Chicago

Cengellenmis, Yasemin, and Abdullah Dertli. 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.

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

[1]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, Apr. 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 1, 2019): 87-93. https://doi.org/10.36753/mathenot.559260.

JAMA

1.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, Apr. 2019, pp. 87-93, doi:10.36753/mathenot.559260.

Vancouver

1.Yasemin Cengellenmis, Abdullah Dertli. The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p. Math. Sci. Appl. E-Notes. 2019 Apr. 1;7(1):87-93. doi:10.36753/mathenot.559260