On MDS convolutional codes over Z_p^r

Maximum distance separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in Oued and Sole (IEEE Trans Inf Theory 59(11):7305–7313, 2013) via...

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Bibliographic Details
Main Author: Pinto, Raquel (author)
Other Authors: Napp, Diego (author), Toste, Marisa (author)
Format: article
Language:eng
Published: 1000
Subjects:
Convolutional codes over finite rings
Free distance
MDS codes
Singleton bound
p-Basis
Online Access:http://hdl.handle.net/10773/16187
Country:Portugal
Oai:oai:ria.ua.pt:10773/16187
Description
Summary:Maximum distance separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in Oued and Sole (IEEE Trans Inf Theory 59(11):7305–7313, 2013) via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Zpr 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 Zpr for any given set of parameters.

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