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MDS 2D convolutional codes with optimal 1D horizontal projections

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Abstract

Two dimensional (2D) convolutional codes is a class of codes that generalizes standard one-dimensional (1D) convolutional codes in order to treat two dimensional data. In this paper we present a novel and concrete construction of 2D convolutional codes with the particular property that their projection onto the horizontal lines yield optimal [in the sense of Almeida et al. (Linear Algebra Appl 499:1–25, 2016)] 1D convolutional codes with a certain rate and certain Forney indices. Moreover, using this property we show that the proposed constructions are indeed maximum distance separable, i.e., are 2D convolutional codes having the maximum possible distance among all 2D convolutional codes with the same parameters. The key idea is to use a particular type of superregular matrices to build the generator matrix.

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Acknowledgements

The authors are grateful to the anonymous referees for the many insightful comments. 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-Fundação para a Ciência e a Tecnologia), within Project UID/MAT/04106/2013.

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Authors and Affiliations

  1. CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paulo Almeida, Diego Napp & Raquel Pinto

Authors
  1. Paulo Almeida
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  2. Diego Napp
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  3. Raquel Pinto
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Correspondence to Raquel Pinto.

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This is one of several papers published in Designs, Codes and Cryptography comprising the Special Issue on Network Coding and Designs.

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Almeida, P., Napp, D. & Pinto, R. MDS 2D convolutional codes with optimal 1D horizontal projections. Des. Codes Cryptogr. 86, 285–302 (2018). https://doi.org/10.1007/s10623-017-0357-1

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  • DOI: https://doi.org/10.1007/s10623-017-0357-1

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