Quantum Codes From Cyclic Codes Over The Ring R 2

Let R ₂ denotes the ring F ₂ + μF ₂ + υ₂ + μυ F ₂ + wF ₂ + μwF ₂ + υwF ₂ + μυwF₂. In this study, we construct quantum codes from cyclic codes over the ring R₂, for arbitrary length n, with the restrictions μ² = 0, υ² = 0, w ² = 0, μυ = υμ, μw = wμ, υw = wυ and μ (υw) = (μυ) w. Also, we give a necessary and sufficient condition for cyclic codes over R₂ that contains its dual. As a final point, we obtain the parameters of quantum error-correcting codes from cyclic codes over R 2 and we give an example of quantum error-correcting codes form cyclic codes over R ₂. (paper)