Prikladnaya Diskretnaya Matematika. Supplement
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Prikladnaya Diskretnaya Matematika. Supplement, 2019, Issue 12, Pages 111–113
DOI: https://doi.org/10.17223/2226308X/12/34
(Mi pdma449)
 

Mathematical Methods of Cryptography

Homogeneous matroids and block-schemes

N. V. Medvedev, S. S. Titov

Urals State University of Railway Transport, Ekaterinburg
References:
Abstract: 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.
Keywords: secret sharing schemes, homogeneous matroids, block-schemes, cycles, Steiner triple systems.
Bibliographic databases:
Document Type: Article
UDC: 519.151, 519.725, 519.165
Language: Russian
Citation: N. V. Medvedev, S. S. Titov, “Homogeneous matroids and block-schemes”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 111–113
Citation in format AMSBIB
\Bibitem{MedTit19}
\by N.~V.~Medvedev, S.~S.~Titov
\paper Homogeneous matroids and block-schemes
\jour Prikl. Diskr. Mat. Suppl.
\yr 2019
\issue 12
\pages 111--113
\mathnet{http://mi.mathnet.ru/pdma449}
\crossref{https://doi.org/10.17223/2226308X/12/34}
\elib{https://elibrary.ru/item.asp?id=41153893}
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    Prikladnaya Diskretnaya Matematika. Supplement
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