<p style='text-indent:20px;'>In this paper, we develop the theory of convolutional codes over finite commutative chain rings. In particular, we focus on maximum distance profile (MDP) convolutional codes and we provide a characterization of these codes, generalizing the one known for fields. Moreover, we relate (reverse) MDP convolutional codes over a finite chain ring with (reverse) MDP convolutional codes over its residue field. Finally, we provide a construction of (reverse) MDP convolutional codes over finite chain rings generalizing the notion of (reverse) superregular matrices.</p>

中文翻译：

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有限链环上的卷积码、MDP码及其表征

<p style='text-indent:20px;'>在本文中，我们发展了有限交换链环上的卷积码理论。特别是，我们专注于最大距离分布 (MDP) 卷积码，并提供这些码的特征，概括已知的领域。此外，我们将有限链环上的（反向）MDP 卷积码与其残差域上的（反向）MDP 卷积码相关联。最后，我们提供了一种在有限链环上的（反向）MDP卷积码的构造，推广了（反向）超正则矩阵的概念。</p>