to very weak bounds. In this paper, we also present bounds for the necessary field size for complete MDP convolutional codes.

Since constructions - especially over fields of possibly small size - have been found to be very hard to obtain, it is an interesting question, how large the probability for an MDP respective complete MDP convolutional code is, when choosing the code randomly. In this paper, we give lower bounds for this probability for MDP as well as for complete MDP convolutional codes.

The paper is structured as follows. In Section 2, we start with some preliminaries about MDP convolutional codes. In Section 3, we give the exact minimum field size for $(n,1,1)$ (and $(n,n-1,1)$) MDP, reverse MDP and complete MDP convolutional codes as well as the corresponding probabilities. In Section 4, we show upper bounds for the necessary field size for MDP convolutional codes and lower bounds for the probability that a convolutional code is MDP. In Section 5, we generalize the results of Section 4 to complete MDP convolutional codes. Section 6 provides an improved bound on the field size for MDP convolutional codes in the case $\delta<\max\{k,n-k\}$. In Section 7, we show that except for very 