In this paper, we study the conditions for a convolutional code to be MDP in terms of the size of the base field ${\mathbb{F}}_q$ as well as the openness of the MDP property in a given family of convolutional codes. Given $(n,k,\delta )$, our main result is an explicit bound depending on $(n,k,\delta )$ such that if q is greater than this bound, there exists a $(n,k,\delta )$ MDP convolutional code. A similar result is also offered for complete MDP convolutional codes. We show that these bounds are much lower than that those appeared so far in the literature. Finally, we show an explicit and simple construction procedure for MDP convolutional Goppa codes of dimension one.

在本文中，我们根据基场的大小研究了卷积码成为 MDP 的条件 ${\mathbb{F}}_q$以及给定卷积码族中 MDP 属性的开放性。给定的$(n,克,\delta )$，我们的主要结果是一个明确的界限，取决于 $(n,克,\delta )$使得如果q大于这个界限，则存在一个$(n,克,\delta )$MDP 卷积码。对于完整的 MDP 卷积码，也提供了类似的结果。我们表明，这些界限远低于目前文献中出现的界限。最后，我们展示了一个一维 MDP 卷积 Goppa 码的明确而简单的构造过程。