CONVOLUTIONAL CODES OVER FINITE CHAIN RINGS, MDP CODES AND THEIR CHARACTERIZATION

被引：3

作者：

Alfarano, Gianira N. ^{[1
]}

Gruica, Anina ^{[2
]}

Lieb, Julia ^{[1
]}

Rosenthal, Joachim ^{[1
]}

机构：

[1] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, De Groene Loper 5, NL-5612 AZ Eindhoven, Netherlands

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2023年 / 17卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

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

D O I：

10.3934/amc.2022028

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：1 / 22

页数：22

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