  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.
