Exponential families and linear codes

In this talk we establish a connection between exponential families of k-interactions, 0/1 polytopes and linear codes. We will see how we can map exponential families in a "face"-preserving way, and study a nice convex polytope instead of the closure of a twisted exponential family. Furthermore the coordinates of vertices of this polytopes turn out to form a so called linear code, which is a subspace of the finite vector space $(F_2)^N$.