English

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.

Keywords

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

R2 v1 2026-06-24T01:20:27.535Z