Codes and anticodes in the Grassman graph

Authors:
Moshe Schwartz;Tuvi Etzion
Affiliations:
Department of Computer Science, Technion--Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion--Israel Institute of Technology, Haifa, Israel
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

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Abstract

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.