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

Gianira N. Alfarano; Anina Gruica; Julia Lieb; Joachim Rosenthal

doi:10.3934/amc.2022028

Article Contents

2023, Volume 17, Issue 1: 1-22. Doi: 10.3934/amc.2022028 open access

This issue Previous Article Preface Next Article On the computational hardness of the code equivalence problem in cryptography

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

1.
Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
2.
Department of Mathematics and Computer Science, Eindhoven University of Technology, De Groene Loper 5, 5612 AZ Eindhoven, the Netherlands

^* Corresponding author: Gianira N. Alfarano
^* Corresponding author: Gianira N. Alfarano

Received: May 2021

Revised: March 2022

Early access: April 2022

Published: December 2022

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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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Mathematics Subject Classification: 15B33, 94B10, 15B05, 11T71.

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