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

Gianira N. Alfarano (Corresponding author), 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.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalAdvances in Mathematics of Communications
Volume17
Issue number1
DOIs
Publication statusPublished - Feb 2023

Bibliographical note

Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.

Funding

Acknowledgments. This work was partially supported by Swiss National Science Foundation grant n. 188430. The authors are thankful to Alessandro Neri for fruitful comments and discussion and to the anonymous reviewers whose comments contributed to improve the paper.

FundersFunder number
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung188430

    Keywords

    • Convolutional codes
    • finite chain rings
    • MDP convolutional codes
    • reverse superregular matrices
    • superregular matrices

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