Convolutional codes over finite chain rings, MDP codes and their characterization
Information Theory
2022-03-31 v2 math.IT
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.
Cite
@article{arxiv.2104.09486,
title = {Convolutional codes over finite chain rings, MDP codes and their characterization},
author = {Gianira N. Alfarano and Anina Gruica and Julia Lieb and Joachim Rosenthal},
journal= {arXiv preprint arXiv:2104.09486},
year = {2022}
}
Comments
19 pages