A computational technique for determining rate regions for networks and multilevel diversity coding systems based on inner and outer bounds for the region of entropic vectors is discussed. The expression to get rate region in terms of region of entropic vectors is attributed to Yeung and Zhang. An inner bound based on binary representable matroids is discussed that has the added benefit of identifying optimal linear codes. The theorem stated by Hassibi et al. in 2010 ITA is implemented to get H-representation of binary matroid inner bound for more than 4 variables. The computational technique is demonstrated on a series of small examples of multilevel diversity coding systems.