Quantum Codes

Abstract

In the present paper, the quantum codes over F_q which are obtained from cyclic codes over the finite ring R=F_q+uF_q +vF_q+uvF_q+v²F_q+uv²F_q with u²=1,v³=v ,uv=vu where q=p^m and p is an odd prime. Moreover the parameters of quantum codes over F_q are determined. Some examples are given.

Keywords

• Qunatum codes,Gray map,cyclic codes

Kuantum Kodlar

Abstract

Bu çalışmada,u²=1,v³=v ,uv=vu,q=p^m   ve p tek asal sayı olmak üzere R=F_q+uF_q +vF_q+uvF_q+v²F_q+uv²F_q    halkası üzerindeki devirli kodlar kullanılarak F_q üzerindeki kuantum kodlar elde edildi. Ayrıca, F_q üzerindeki kuantum kodların parametreleri belirlendi. Bazı örnekler verildi

Keywords

• Kuantum kodlar,devirli kodlar,Gray dönüşümü

References

1. Ashraf M, Mohammad G, 2014. Quantum codes from cyclic codes over . International Journal of Quantum Information, 12 (6):1450042.
2. Ashraf M, Mohammad G, 2015. Construction of quantum codes from cyclic codes over . International Journal of Information and Coding Theory, 2 : 137-144. Ashraf M, Mohammad G, Quantum codes from cyclic codes over . Quantum Information Processing, DOI:10.1007/s11128-016-1379-8.
3. Calderbank A R, Rains E M, Shor P M, Sloane N J A, 1998. Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory, 44:1369-1387.
4. Dertli A, Cengellenmis Y, Eren S, 2015a. On quantum codes obtained from cyclic codes over . International Journal of Quantum Information, 13: 1550031.
5. Dertli A, Cengellenmis Y, Eren S, 2015b. Quantum Codes over the Ring . International Journal of Algebra, 9: 115-121.
6. Dertli A, Cengellenmis Y, Eren S, 2016a. On the linear codes over the ring . Discrete Mathematics, Algorithms and Applications, 1650036.
7. Dertli A, Cengellenmis Y, Eren S, 2015c. On the Codes over a Semilocal Finite Ring. Intern. J. of Adv. Computer Science & Application, DOI: 10.14569/IJACSA.2015.061038.
8. Dertli A, Cengellenmis Y, Eren S, 2016b. Some results on the linear codes over the finite ring . International Journal of Quantum Information, 1650012.

9. Dertli A, Cengellenmis Y, Eren S, 2015d. Quantum Codes Over . Palestine Journal of Mathematics, 4: 547-552.
10. Kai X, Zhu S, 2011. Quaternary construction bof quantum codes from cyclic codes over . International Journal of Quantum Information, 9:689-700.
11. Liu Y, Shi M, Lu Z, 2017. Skew cyclic codes over . IEICE Transactions Fundamentals, DOI:101587/transfun.E0.A.1.
12. Qian J, 2013. Quantum codes from cyclic codes over . Journal of Information computational Science, 10:1715-1722.
13. Qian J, Ma W, Gou W, 2009. Quantum codes from cyclic codes over finite ring. International Journal of Quantum Information, 7:1277-1283.
14. Shor P W, 1995. Scheme for reducing decoherence in quantum memory. Phys. Rev. A, 52:2493-2496.
15. Steane A M, 1996. Simple quantum error correcting codes. Phys. Rev. A, 54:4741-4751.
16. Yin X, Ma W, 2011. Gray map and quantum codes over the ring . In Trust, Security and Privacy in Computing and Communications (TrustCom). IEEE 10th International Conference on, p:897-899.