On MDS convolutional Codes over $\mathbb Z_{p^r}$
Information Theory
2016-01-19 v1 math.IT
Rings and Algebras
Abstract
Maximum Distance Separable (MDS) convolutional codes are cha- racterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Z p r was recently discovered in [26] via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Z p r from a new perspective. We introduce the notions of p-standard form and r- optimal parameters to derive a novel upper bound of Singleton type on the free distance. Moreover, we present a constructive method for building general (non necessarily free) MDS convolutional codes over Z p r for any given set of parameters.
Cite
@article{arxiv.1601.04507,
title = {On MDS convolutional Codes over $\mathbb Z_{p^r}$},
author = {Diego Napp and Raquel Pinto and Marisa Toste},
journal= {arXiv preprint arXiv:1601.04507},
year = {2016}
}