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On the representability of the biuniform matroid
Ball, Simeon Michael; Padró Laimon, Carles; Weiner, Zsuzsa; Xing, Chaoping
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
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
Peer Reviewed
Àrees temàtiques de la UPC::Informàtica::Seguretat informàtica::Criptografia
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Combinatorial analysis
matroid theory
representable matroid
biuniform matroid
secret sharing

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