  In 1991, Wei introduced generalized minimum Hamming weights for linear codes
and showed their monotonicity and duality. Recently, several authors extended
these results to the case of generalized minimum poset weights by using
different methods. Here, we would like to prove the duality by using matroid
theory. This gives yet another and very simple proof of it. In particular, our
argument will make it clear that the duality follows from the well-known
relation between the rank function and the corank function of a matroid. In
addition, we derive the weight distributions of linear MDS and Near-MDS poset
codes in the same spirit.
