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arXiv · 2104.09486

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

Gianira N. Alfarano·Anina Gruica·Julia Lieb·Joachim Rosenthal
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Abstract

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.

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Gianira N. Alfarano, Anina Gruica, Julia Lieb, Joachim Rosenthal. 2021-04-19. Convolutional codes over finite chain rings, MDP codes and their characterization. https://arxiv.org/abs/2104.09486

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