ACD codes over Z2R. and the MacWilliams identities

Additive complementary dual (in short, ACD) codes are considered over the ring Z(2)R, = Z(2) x Z(2)[u]/< u(4)>. We investigate free self-dual codes over R. A condition that ensures an additive code to be an ACD code is established. Furthermore, for a separable additive code to be an ACD code, a necessary and sufficient condition is obtained. We study a Gray map under which certain additive codes become binary linear complementary dual (in short, LCD) codes. We also present a few optimal (or almost optimal) binary LCD codes. Moreover, a number of weight enumerators are computed and the corresponding MacWilliams identities are discussed.