  It has been shown that maximum distance profile (MDP) convolutional codes
have optimal recovery rate for windows of a certain length, when transmitting
over an erasure channel. In addition, the subclass of complete MDP
convolutional codes has the ability to reduce the waiting time during decoding.
In this paper, we derive upper bounds on the necessary field size for the
existence of MDP and complete MDP convolutional codes and show that these
bounds improve the already existing ones. Moreover, we derive lower bounds for
the probability that a random code is MDP respective complete MDP.
