Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the representability of the bi-uniform matroid   Every bi-uniform 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
bi-uniform 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 bi-uniform matroids is proved here for the first
time. The previously known efficient constructions apply only to a particular
class of bi-uniform 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.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an