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

Year 2019, , 87 - 93, 30.04.2019

Yasemin Cengellenmis Abdullah Dertli

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

Cited By: 3

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.