A new construction method for networks from matroids

We study the problem of information flow in communication networks with noiseless links in which the dependency relations among the data flowing on the different network edges satisfy matroidal constraints. We present a construction that maps any given matroid to a network that admits vector linear network codes over a certain field if and only if the matroid has a multilinear representation over the same field. This new construction strengthens previous results in the literature and, thus, establishes a deeper connection between network coding and matroid theory. We also explore another, more general, mathematical construct referred to as FD-relation which is more suitable than matroids in capturing the dependency relations in general networks.