On quantum codes obtained from cyclic codes over A2

In this paper, quantum codes from cyclic codes over A 2 = F 2 + uF 2 + vF 2 + uvF 2 , u 2 = u, v 2 = v, uv = vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A 2 , then so is Ψ(C), where Ψ is a Gray map. A necessary and sufficient condition for cyclic codes over A 2 that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A 2 .