Asymptotically Good Additive Cyclic Codes

Z_pZ_p^s-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.