Geodesic
On homogeneous matroids and block-schemes
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 21-23

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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.
Keywords: secret sharing schemes, homogeneous matroids, block-schemes
Mots-clés : circuits. 
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     author = {N. V. Medvedev and S. S. Titov},
     title = {On homogeneous matroids and block-schemes},
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     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a6/}
}
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N. V. Medvedev; S. S. Titov. On homogeneous matroids and block-schemes. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 21-23. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a6/