On homogeneous matroids and block-schemes

This research is devoted to access control through ideal perfect secret sharing schemes and matroids. A matroid is homogeneous if all its circuits have equal cardinality, but possibly not all subsets of this cardinality are circuits. A linkage of such matroids with block-schemes including Steiner triple is revealed. It is proved that any matroid, in which co-hyperplanes are the Steiner triples, is homogeneous connected and separating if its cardinality is not less than seven. It is also proved that block-scheme, in which each pair of different elements appears in a single block, specifies the co-hyperplanes of a homogeneous connected separating matroid. Some hypotheses for further research are presented.