  In this paper we introduce generalized hyperbent functions from $F_{2^n}$ to
$Z_{2^k}$, and investigate decompositions of generalized (hyper)bent functions.
We show that generalized (hyper)bent functions from $F_{2^n}$ to $Z_{2^k}$
consist of components which are generalized (hyper)bent functions from
$F_{2^n}$ to $Z_{2^{k^\prime}}$ for some $k^\prime < k$. For odd $n$, we show
that the Boolean functions associated to a generalized bent function form an
affine space of semibent functions. This complements a recent result for even
$n$, where the associated Boolean functions are bent.
