Abstract
We propose the concept of weight-decomposition construction for perfect secret sharing schemes. This construction is more general than previous constructions. Based on the weight-decomposition construction, we improve the information rate in 4 cases of the left unsolved 18 cases of secret sharing schemes for connected graphs on six vertices. In addition, we also propose some efficient decomposition constructions for perfect secret sharing schemes with access structures of constant rank. Compared with the best previous constructions, our constructions have some improved lower bounds on the information rate.