Defining the q-analogue of a matroid

Abstract

\u3cp\u3eThis paper defines the q-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a q-matroid, and why they are (not) cryptomorphic. Also, we explain the motivation for studying q-matroids by showing that a rank metric code gives a q-matroid.\u3c/p\u3