On optimal constacyclic codes

In this paper we construct new families of maximum-distance-separable (MDS) convolutional codes derived from classical constacyclic codes. Additionally, we also construct new families of almost MDS block and convolutional codes. Most of the new convolutional codes constructed here are unit-memory and have degree γ=2γ=2. Moreover, based on a different method, we construct families of asymmetric quantum codes known in the literature. All these results are mainly derived from the investigation of suitable properties on cyclotomic cosets of such codes.