  Maximum-distance separable (MDS) convolutional codes are characterized by the
property that their free distance reaches the generalized Singleton bound. In
this paper, new criteria to construct MDS convolutional codes are presented.
Additionally, the obtained convolutional codes have optimal first (reverse)
column distances and the criteria allow to relate the construction of MDS
convolutional codes to the construction of reverse superregular Toeplitz
matrices. Moreover, we present some construction examples for small code
parameters over small finite fields.
