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 language | English |
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Pages (from-to) | 1-22 |
Number of pages | 22 |
Journal | Advances in Mathematics of Communications |
Volume | 17 |
Issue number | 1 |
DOIs | |
Publication status | Published - 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.
Funders | Funder number |
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Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | 188430 |
Keywords
- Convolutional codes
- finite chain rings
- MDP convolutional codes
- reverse superregular matrices
- superregular matrices