On paving matroids and a generalization of MDS codes

AbstractWe define a class of codes that corresponds to a class of matroids called paving matroids. This class of codes includes maximum-distance-separable (MDS) codes, and some other interesting codes such as the (12,6) ternary Golay code. Some basic properties of these codes are established using techniques from matroid theory. Our results raise a natural existence question to which we obtain partial answers using known results about the non-existence of Steiner systems of the type S(t–1,t,2t)