On the Representability of the Biuniform Matroid
| Autor: | Chaoping Xing, Carles Padró, Simeon Ball, Zsuzsa Weiner |
|---|---|
| Přispěvatelé: | 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, School of Physical and Mathematical Sciences |
| Rok vydání: | 2013 |
| Předmět: |
Class (set theory)
Combinatorial analysis General Mathematics Weighted matroid Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC] 0102 computer and information sciences 02 engineering and technology biuniform matroid 01 natural sciences Secret sharing Matroid Combinatorics 0202 electrical engineering electronic engineering information engineering Matroides Mathematics Discrete mathematics matroid theory Criptografia 020206 networking & telecommunications Matroids Oriented matroid Graphic matroid Finite field 010201 computation theory & mathematics secret sharing representable matroid Matroid partitioning Informàtica::Seguretat informàtica::Criptografia [Àrees temàtiques de la UPC] Science::Mathematics::Discrete mathematics [DRNTU] |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) SIAM Journal on Discrete Mathematics Recercat. Dipósit de la Recerca de Catalunya Universitat Jaume I |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/120886960 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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