In this paper, we propose a method which enables to construct almost optimal broadcast schemes on an n-dimensional hypercube in the circuit switched,-port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured by a ow technique and results about symmetric ow networks. We apply the method to design optimal schemes improving and generalizing the previous results.