Minimal Realizations of Syndrome Formers of a Special Class of 2D Codes

  • Ettore Fornasini
  • Telma Pinho
  • Raquel PintoEmail author
  • Paula Rocha
Conference paper
Part of the CIM Series in Mathematical Sciences book series (CIMSMS, volume 3)


In this paper we consider a special class of 2D convolutional codes (composition codes) with encoders G(d1, d2) that can be decomposed as the product of two 1D encoders, i.e., \(G(d_{1},d_{2}) = G_{2}(d_{2})G_{1}(d_{1})\). In case that \(G_{1}(d_{1})\) and \(G_{2}(d_{2})\) are prime we provide constructions of syndrome formers of the code, directly from \(G_{1}(d_{1})\) and \(G_{2}(d_{2})\). Moreover we investigate the minimality of 2D state-space realization by means of a separable Roesser model of syndrome formers of composition codes, where \(G_{2}(d_{2})\) is a quasi-systematic encoder.


Encoders and syndrome forms 2D composition codes 2D state-space models 



This work was supported by Portuguese funds through the CIDMA – Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundac̣ão para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ettore Fornasini
    • 1
  • Telma Pinho
    • 2
  • Raquel Pinto
    • 2
    Email author
  • Paula Rocha
    • 3
  1. 1.Department of Information EngineeringUniversity of PaduaPaduaItaly
  2. 2.Center for Research and Development in Mathematics and Applications (CIDMA), Department of MathematicsUniversity of AveiroAveiroPortugal
  3. 3.Research Center for Systems and Technologies, SYSTEC, Faculty of EngineeringUniversity of PortoPortoPortugal

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