  An improved Singleton-type upper bound is presented for the list decoding
radius of linear codes, in terms of the code parameters [n,k,d] and the list
size L. L-MDS codes are then defined as codes that attain this bound (under a
slightly stronger notion of list decodability), with 1-MDS codes corresponding
to ordinary linear MDS codes. Several properties of such codes are presented;
in particular, it is shown that the 2-MDS property is preserved under duality.
Finally, explicit constructions for 2-MDS codes are presented through
generalized Reed-Solomon (GRS) codes.
