  We compute the exact maximum state complexity for the language consisting of
$m$ words of length $N$, and characterize languages achieving the maximum. We
also consider a special case, namely languages $C(w)$ consisting of the
conjugates of a single word $w$. The words for which the maximum state
complexity of $C(w)$ is achieved turn out to be a natural generalization of de
Bruijn words. We show that generalized de Bruijn words exist for each length
and consider the number of them.
