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Title:
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On the representability of the biuniform matroid
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Author:
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Ball, Simeon Michael; Padró Laimon, Carles; Weiner, Zsuzsa; Xing, Chaoping
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
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Abstract:
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Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields.
© 2013, Society for Industrial and Applied Mathematics |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Seguretat informàtica::Criptografia
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
-Combinatorial analysis
-Matroids
-matroid theory
-representable matroid
-biuniform matroid
-secret sharing
-Matroides
-Criptografia |
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Rights:
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Document type:
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Article - Published version
Article |
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