Codes and anticodes in the Grassman graph

摘要

Pet-feet codes and optimal anticodes in the Grassman graph G(q)(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. (C) 2001 Elsevier Science. [References: 6]