  Given a perfect coloring of a graph, we prove that the $L_1$ distance between
two rows of the adjacency matrix of the graph is not less than the $L_1$
distance between the corresponding rows of the parameter matrix of the
coloring. With the help of an algebraic approach, we deduce corollaries of this
result for perfect $2$-colorings, perfect colorings in distance-$l$ graphs and
in distance-regular graphs. We also provide examples when the obtained property
reject several putative parameter matrices of perfect colorings in infinite
graphs.
