Completely regular codes in the Hoffman-Singleton graph

The Hoffman-Singleton graph is a strongly regular graph on 50 vertices of degree 7, which is the Moore graph with the maximum degree among known Moore graphs. A representation of this graph in terms of five non-intersecting subgraphs, which are Petersen graphs, is proposed. All intersection matrices of completely regular codes in the Hoffman-Singleton graph are listed. There are ten such matrices: five matrices of order 2 and five matrices of order 3.