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

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

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

Author(s) -

Gianira N. Alfarano,

Anina Gruica,

Julia Lieb,

Joachim Rosenthal

Publication year - 2022

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2022028

Subject(s) - convolutional code , mathematics , finite field , linear code , serial concatenated convolutional codes , discrete mathematics , block code , combinatorics , algorithm , decoding methods

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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