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 MDP convolutional codes over a finite chain ring with MDP convolutional codes over its residue field. Finally, we provide a construction of MDP convolutional codes over finite chain rings generalizing the notion of superregular matrices.

翻译：在本文中,我们发展了针对有限通量链环的革命守则理论。特别是,我们侧重于最大距离剖面(MDP)革命守则,我们对这些守则进行了定性,概括了已知领域的守则。此外,我们把MDP革命守则与有限链圈联系起来,将MDP革命守则与其残余领域联系起来。最后,我们为有限链圈提供了MDP革命守则的构建,将超常规基质的概念普遍化。