ZpZps-additive cyclic codes have been proved to be asymptotically good by Yao and Zhu.For binary Hamming scheme,we introduce a type of Z2(Z2 + uZ2)-additive cyclic codes generated by pairs of polynomials.Let R be the chain ring Z2 + uZ2,where u2 =0.The asymptotic rates and relative distances of this class of codes are presented by establishing the relationship between the random Z2R-additive cyclic code and random binary quasi-cyclic code of index 2.We show that Z2R-additive cyclic codes are asymptotically good.