  Let $\chi'_d(n,q)$ (resp. $\chi_d(n,q)$) denote the minimum number of colors
necessary to color a $q$-ary $n$-cube so that no two vertices that are at a
distance at most $d$ (resp. exactly $d$) get the same color. These two problems
were proposed in the study of scalability of optical networks. In this paper,
we provide upper and lower bounds on $\chi'_d(n,q)$ and $\chi_d(n,q)$ when $q$
is a prime power.
