On near-MDS codes

Considers a family of codes obtained by weakening the restrictions in the definition of classical maximum-distance-separable (MDS) codes. This family of codes, which the authors call near-MDS (NMDS) contains remarkable representatives such as the ternary Golay codes, the quaternary quadratic-residue [11,6,5] and extended quadratic-residue [12,6,6] codes, as well as a large number of algebraic geometric (AG) codes. There exist interesting connections of NMDS codes with area in finite projective geometries, as well as with combinatorial designs.<>