On equitable partitions of $q$-ary Hamming graphs

Methods for constructing perfect colorings in $H(n,q)$ are considered. At this seminar, the constructions were considered for non-prime $q$, based on the Kronecker product.
A direct construction allows one to construct a perfect coloring of the graph $H(n,pq)$ with the parameters $[[pa+n(p-1),pb],[pc,pd+n(p-1)]]$ from a perfect coloring $H(n,q)$ with parameters $[[a,b],[c,d]]$. As it turned out in the course of the discussion, in some cases it is possible to construct another coloring with new parameters on the basis of splitting one of the colors of the resulting coloring (the first example is a coloring with parameters $[[6.3], [5.7]]$ in $H(3,4))$.