  In this paper we investigate the class of constacyclic codes, which is a
natural generalization of the class of cyclic and negacyclic codes. This class
of codes is interesting in the sense that it contains codes with good or even
optimal parameters. In this light, we propose constructions of families of
classical block and convolutional maximum-distance-separable (MDS) constacyclic
codes, as well as families of asymmetric quantum MDS codes derived from
(classical-block) constacyclic codes. These results are mainly derived from the
investigation of suitable properties on cyclotomic cosets of these
corresponding codes.
