Gray Map and Quantum Codes over the Ring F_2+uF_2+u^2F_2

In this paper, by defining the Lee distance and the Lee weight of linear codes over the ring R=F_2+uF_2+u^2F_2, we construct a Gray map which is both an isometry and a weight-preserving map from R^n to F_2^{3n}. In addition, using the proposed Gray map, we give an existence condition of quantum codes which are derived from cyclic codes over R with the Lee metric.