Optimal constant weight codes over \(Z_k\) and generalized designs (Q1357723)

Optimal constant weight codes over arbitrary alphabets are considered in this paper; some are derived from various block designs, including generalized \(t\)-designs, or \(H\)-designs, using notation of \textit{W. H. Mills} [Proc. 5th Southeastern Conf. Comb., Graph Theor., Comput., Boca Raton 1974, 573-581 (1974; Zbl 0308.05009)]. Codes which form generalized Steiner systems with their supports forming ordinary Steiner systems are considered, as well as classes of codes which are MDS constant weight codes. The paper concludes with a list of open problems.