$|\mathbb F|>\min\{M_1,M_2,M_3\}$).

It has already been shown that $M_1$, $M_2$ and $M_3$ are upper bounds for $\deg(g)$.

By the Schwartz-Zippel, the probability that the variables do not fulfill the condition for MDP is upper bounded by $\deg(g)\cdot t$.\
One has to consider conditional probability with the condition that $Q$ and $P$ are left coprime. Therefore, the overall probability is upper bounded by the absolute probability divided by the probability of the condition, which is $1-t^k+O(t^{k+1})$; see [@ich].

Sufficient field size and probability for complete MDP convolutional codes
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In this section, we want to do the same considerations for complete MDP convolutional codes that were done for MDP convolutional codes in the preceding section.

Sufficient field size
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Let $f$ be the polynomial that is formed by the product of all not trivially zero fullsize minors of $\mathfrak{H}$ and has the entries of the coefficient matrices of $H$ as variables. Then, for $(n-k)\mid\delta$, an $(n,k,\delta)$ complete MDP convolutional code exists if $|\mathbb F|>\deg(f)$.

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One uses Schwartz-Zippel and proceeds completely analogous to the preceding subsection.

Again, we have to estimate the degree of the polynomial $f$ from the preceding theorem to get an explicite bound for the field size.

 