A note on secret sharing schemes with three homogeneous access structure

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. The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. This paper deals with these problems for 3-homogeneous access structures, that is, whenever the minimal qualified subsets have exactly three participants.