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Designs, Codes and Cryptography

Erschienen in:

01.01.2014

Realization of 2D convolutional codes of rate \(\frac{1}{n}\) by separable Roesser models

verfasst von: Telma Pinho, Raquel Pinto, Paula Rocha

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1-2/2014

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Abstract

In this paper, two-dimensional convolutional codes constituted by sequences in \((\mathbb F ^n)^{\mathbb{Z }^{2}}\) where \(\mathbb F \) is a finite field, are considered. In particular, we restrict to codes with rate \(\frac{1}{n}\) and we investigate the problem of minimal dimension for realizations of such codes by separable Roesser models. The encoders which allow to obtain such minimal realizations, called R-minimal encoders, are characterized.

Vorheriger Artikel Modified Niederreiter type of GPT cryptosystem based on reducible rank codes

A polynomial matrix \(G(z_1,z_2)\in \mathbb F [z_1,z_2]^{n \times k}\) is right factor prime if for every factorization \(G(z_1,z_2)=\bar{G}(z_1,z_2)T(z_1,z_2),\) with \(\bar{G}(z_1,z_2)\in \mathbb F [z_1,z_2]^{n \times k}\) and \(T(z_1,z_2)\in \mathbb F [z_1,z_2]^{k \times k},\) \(T(z_1,z_2)\) is unimodular (i.e., it is invertible in \(\mathbb F [z_1,z_2]^{k \times k}\)).

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Titel: Realization of 2D convolutional codes of rate by separable Roesser models
verfasst von: Telma Pinho
Raquel Pinto
Paula Rocha
Publikationsdatum: 01.01.2014
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1-2/2014
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-012-9768-1

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