On homogeneous matroid ports

Abstract

A matroid port is a clutter (antichain of sets) determined by the collection of circuits of a matroid that contain a fixed point. We study the problem of determining matroid ports all whose elements have the same size h. This problem has been studied from the cryptographic perspective and it is related to an analogous problem in matroid theory. We give some general results and then focus on the binary case. We recast some known results and find all 4-homogeneous binary matroid ports.