Recursive constructions for perfect secret sharing schemes

A secret sharing scheme is a method which allows a secret to be shared among a set of participants in such a way that only qualified subsets of participants can recover the secret. A secret sharing scheme is called perfect if unqualified subsets of participants obtain no information regarding the secret. The information rate of a secret sharing scheme is defined to be the ratio between the size of secret and the maximum size of the shares. In this paper, we propose some recursive 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.