Codes and Anticodes in the Grassman Graph

Perfect codes and optimal anticodes in the Grassman graph Gq(n, k) are examined. It is shown that the vertices of the Grassman graph cannot be partitioned into optimal anticodes, with a possible exception when n=2k. We further examine properties of diameter perfect codes in the graph. These codes are known to be similar to Steiner systems. We discuss the connection between these systems and “real” Steiner systems.