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Designs, Codes and Cryptography

, Volume 70, Issue 1–2, pp 241–250 | Cite as

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

  • Telma Pinho
  • Raquel PintoEmail author
  • Paula Rocha
Article

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.

Keywords

2D Convolutional codes Minimal realizations Separable Roesser model 

Mathematics Subject Classification (2000)

93B20 94B10 

Notes

Acknowledgments

The work of the authors was partially supported by FEDER founds through COMPETE-Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese founds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Center for Research and Development in Mathematics and Applications and Department of Electrical and Computer Engineering, Faculty of EngineeringUniversity of OportoPortoPortugal

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