Optimal constant weight codes over Z(k) and generalized designs

We consider optimal constant weight codes over arbitrary alphabets. Some of these codes are derived from good codes over the same alphabet, and some of these codes are derived from block design. Generalizations of Steiner systems play an important role in this context. We give several construction methods for these generalizations. An interesting class of codes are those which form generalized Steiner systems and their supports form ordinary Steiner systems. Finally, we consider classes of codes which are MDS constant weight codes.