Random generation of representable matroids

Matroids in mathematics are finite combinatorial structures with several applications among which are Secret Sharing Schemes (SSS). If V is a vector space over a finite field K, U subset of V is a vector subspace with dim(U) <= dim(V), and J is the collection of linearly independent subsets of U in V, then the pair (V, J) is a matroid, called matroid of l.i. sets in U. All matroids isomorphic to matroids of l.i. sets are said to be representable and those are the basis to obtain ideal SSS. Here we show some procedures embedded into a computational system to generate randomly representable matroids with uniform distribution. We will show some obtained results in our implementation.