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 problems i...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/101419 http://hdl.handle.net/10220/18666 |
| Summary: | 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. |
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