Linear representations of convolutional codes over rings
Optimization and Control
2016-09-19 v1 Information Theory
Commutative Algebra
math.IT
Abstract
In this paper we extend the relation between convolutional codes and linear systems over finite fields to certain commutative rings through first order representations . We introduce the definition of rings with representations as those for which these representations always exist, and we show that finite products of finite fields belong to this class. We develop the input/state/output representations for convolutional codes over these rings, and we show how to use them to construct observable convolutional codes as in the classical case.
Cite
@article{arxiv.1609.05043,
title = {Linear representations of convolutional codes over rings},
author = {Miguel V. Carriegos and Noemí DeCastro-García and Ángel Luis Muñoz Castañeda},
journal= {arXiv preprint arXiv:1609.05043},
year = {2016}
}