  We propose a new way to construct a multicast coding scheme for linear
deterministic relay networks. Our construction can be regarded as a
generalization of the well-known multicast network coding scheme of Jaggi et
al. to linear deterministic relay networks and is based on the notion of flow
for a unicast session that was introduced by the authors in earlier work. We
present randomized and deterministic polynomial--time versions of our algorithm
and show that for a network with $g$ destinations, our deterministic algorithm
can achieve the capacity in $\left\lceil \log(g+1)\right\rceil $ uses of the
network.
