Convolutional codes over finite chain rings, MDP codes and their characterization

04/19/2021

∙

by   Gianira N. Alfarano, et al.

∙

0

∙

share

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.