  The correspondence between linear codes and representable matroids is well
known. But a similar correspondence between quantum codes and matroids is not
known. We show that representable symplectic matroids over a finite field
$\mathbb{F}_q$ correspond to $\mathbb{F}_q$-linear quantum codes. Although this
connection is straightforward, it does not appear to have been made earlier in
literature. The correspondence is made through isotropic subspaces. We also
show that the popular Calderbank-Shor-Steane (CSS) codes are essentially the
homogenous symplectic matroids while the graph states, which figure so
prominently in measurement based quantum computation, correspond to a special
class of symplectic matroids, namely Lagrangian matroids. This association is
useful in that it enables the study of symplectic matroids in terms of quantum
codes and vice versa. Furthermore, it has application in the study of quantum
secret sharing schemes.
