New general lower bounds on the information rate of secret sharing schemes

Abstract

We use two combinatorial techniques to apply a decompo­sition construction in obtaining general lower bounds on information rate and average information rate of certain genera] classes of access structures. The first technique uses combinatorial designs (in particular, Steiner systems S(t, k, u)). The second technique uses equitable edge- colourings of bipartite graphs. For uniform access structures of rank t, this second technique improves the best previous general bounds by a factor of t (asymptotically).