Perfect multiple coverings of hypercube

A subset $C$ of graph vertices is called a perfect $k$-multiple covering with a radius $r$ if every vertex of this graph is within distance $r$ from exactly $k$ vertices of $C$. We give a criterion based on parameters of a perfect coloring. This criterion determines whether the perfect coloring is a perfect multiple covering with fixed radius $r\geq1$ of some multiplicity. Bibliogr. 13.