possible since permutation of the columns of the parity-check matrix does not influence the MDP property. With these definitions/settings, one gets the following theorem:

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Let $\mathbb F$ be finite with cardinality $|\mathbb F|=t^{-1}$. If $|\mathbb F|>\min\{M_1,M_2,M_3\}$, the probability for an MDP convolutional code is lower bounded by\
(i) $1-\frac{(L+1)(n-k)\binom{(L+1)n}{(L+1)(n-k)}\cdot t}{1-t^k+O(t^{k+1})}$\
(ii) $1-\frac{\left((L+1)(n-k)\binom{n}{n-k}\binom{n+k}{n-k}\cdots\binom{n+Lk}{n-k}\right)\cdot t}{1-t^k+O(t^{k+1})}$\
(iii) $1-\frac{\left((L+1)(n-k)\sum_{i=n-k}^{n}\binom{i-1}{n-k-1}\binom{2n-i}{n-k}\cdots\binom{2n+(L-1)k-i}{n-k}\right)\cdot t}{1-t^k+O(t^{k+1})}$

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For MDP (in contrast to complete MDP) it is not necessary that $H$ has generic row degrees. Therefore, one has to make the following considerations for all possible values of the row degrees. However, we will see that this does not matter.

Again, we assume that $H=[P\ Q]$ has the form of Remark \[kh\]. If the row degrees of $Q$ are fixed, one knows for each entry of $H$ either its degree or an upper bound on its degree. Hence, when considering the entries of the coefficient matrices of $H$ as variables, we know how many variables we have and could apply Theorem \[sz\] (b) to the polynomial $g$ that is formed by the product of the non-trivially fullsize minors of $\mathcal{H}_L$. Note that this polynomial is not the zero polynomial (since the existence of MDP convolutional codes has been shown for 