Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/120886960 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | Field | DocType |
matroid theory,representable matroid,biuniform matroid,secret sharing | Matroid,Discrete mathematics,Finite field,Combinatorics,Secret sharing,Oriented matroid,Matroid partitioning,Graphic matroid,Weighted matroid,Mathematics | Journal |
Volume | Issue | ISSN |
27 | 3 | 0895-4801 |
Citations | PageRank | References |
1 | 0.35 | 17 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simeon Ball | 1 | 133 | 28.98 |
| Carles Padró | 2 | 490 | 32.23 |
| Zsuzsa Weiner | 3 | 50 | 9.72 |
| Chaoping Xing | 4 | 916 | 110.47 |