  Maddah-Ali and Niesen's original coded caching scheme for shared-link
broadcast networks is now known to be optimal to within a factor two, and has
been applied to other types of networks. For practical reasons, this paper
considers that a server communicates to cache-aided users through $H$
intermediate relays. In particular, it focuses on combination networks where
each of the $K = \binom{H}{r}$ users is connected to a distinct $r$-subsets of
relays. By leveraging the symmetric topology of the network, this paper
proposes a novel method to general multicast messages and to deliver them to
the users. By numerical evaluations, the proposed scheme is shown to reduce the
download time compared to the schemes available in the literature. The idea is
then extended to decentralized combination networks, more general relay
networks, and combination networks with cache-aided relays and users. Also in
these cases the proposed scheme outperforms known ones.
