On the representability of the biuniform matroid
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 probl...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/24101 |
| Acceso en línea: | https://hdl.handle.net/2117/24101 https://dx.doi.org/10.1137/120886960 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorial analysis Matroids matroid theory representable matroid biuniform matroid secret sharing Matroides Criptografia Àrees temàtiques de la UPC::Informàtica::Seguretat informàtica::Criptografia Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Sumario: | 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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