Homogeneous matroids and block-schemes

This paper concerns the homogeneous matroids in which all the cycles have the same power. The research is related to the problem of describing homogeneous matroids corresponding to ideal homogeneous secret sharing schemes. A possibility for representing the family of cohyperplanes of a homogeneous matroid like blocks of blocks-schemes including the Steiner triple systems is shown. It is proved that a separating matroid is a homogeneous matroid with three-element cohyperplanes, if and only if its cohyperplanes form Steiner triple systems.

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