Objective & Hypothesis:In the present paper, the quantum codes over F q which are obtained from cyclic codes over the finite ring R=F q +u F q +v F q +uv F q +v 2 F q +uv 2 F q with u 2 =1,v 3 =v ,uv=vu where q=p m and p i s an odd prime.
📊
Key Findings & Data:Moreover the parameters of quantum codes over F q are determined.
In the present paper, the quantum codes over F q which are obtained from cyclic codes over the finite ring R=F q +u F q +v F q +uv F q +v 2 F q +uv 2 F q with u 2 =1,v 3 =v ,uv=vu where q=p m and p i s an odd prime. Moreover the parameters of quantum codes over F q are determined. Some examples are given.
Özet
Bu çalışmada,u 2 =1,v 3 =v ,uv=vu,q=p m ve p tek asal sayı olmak üzere R=F q +u F q +v F q +uv F q +v 2 F q +uv 2 F q halkası üzerindeki devirli kodlar kullanılarak F q üzerindeki kuantum kodlar elde edildi. Ayrıca, F q üzerindeki kuantum kodların parametreleri belirlendi. Bazı örnekler verildi
Ashraf M, Mohammad G, 2014. Quantum codes from cyclic codes over. International Journal of Quantum Information, 12 (6):1450042.
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.
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.
Dertli A, Cengellenmis Y, Eren S, 2015a. On quantum codes obtained from cyclic codes over. International Journal of Quantum Information, 13: 1550031.
Dertli A, Cengellenmis Y, Eren S, 2015b. Quantum Codes over the Ring. International Journal of Algebra, 9: 115-121.
Dertli A, Cengellenmis Y, Eren S, 2016a. On the linear codes over the ring. Discrete Mathematics, Algorithms and Applications, 1650036.
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.
Dertli A, Cengellenmis Y, Eren S, 2016b. Some results on the linear codes over the finite ring. International Journal of Quantum Information, 1650012.
Dertli A, Cengellenmis Y, Eren S, 2015d. Quantum Codes Over. Palestine Journal of Mathematics, 4: 547-552.
Kai X, Zhu S, 2011. Quaternary construction bof quantum codes from cyclic codes over. International Journal of Quantum Information, 9:689-700.
Liu Y, Shi M, Lu Z, 2017. Skew cyclic codes over. IEICE Transactions Fundamentals, DOI:101587/transfun.E0.A.1.
Qian J, 2013. Quantum codes from cyclic codes over. Journal of Information computational Science, 10:1715-1722.
Qian J, Ma W, Gou W, 2009. Quantum codes from cyclic codes over finite ring. International Journal of Quantum Information, 7:1277-1283.
Shor P W, 1995. Scheme for reducing decoherence in quantum memory. Phys. Rev. A, 52:2493-2496.
Steane A M, 1996. Simple quantum error correcting codes. Phys. Rev. A, 54:4741-4751.
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.