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.
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Keywords
схемы разделения секрета, однородные матроиды, блок-схемы, циклы, secret sharing schemes, homogeneous matroids, block-schemes, circuitsAuthors
| Name | Organization | |
| Medvedev N. V. | Ural State University of Railways | itcrypt@gmail.com |
| Titov S. S. | Ural State University of Railways | stitov@usaaa.ru |
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