On the connectivity function of a matroid

The connectivity function k of a matroid M on a set E is defined by k(X) = r(X) + r(E − X) − r(E) (X ⊆ E), where r is the rank function. W. H. Cunningham conjectured that a connected matroid is determined, up to duality, by a knowledge of its connectivity function. This is false in general, but true for binary matroids.