  MDS convolutional codes have the property that their free distance is maximal
among all codes of the same rate and the same degree. In this paper we
introduce a class of MDS convolutional codes whose column distances reach the
generalized Singleton bound at the earliest possible instant. We call these
codes strongly MDS convolutional codes. It is shown that these codes can decode
a maximum number of errors per time interval when compared with other
convolutional codes of the same rate and degree. These codes have also a
maximum or near maximum distance profile. A code has a maximum distance profile
if and only if the dual code has this property.
