Fast decoding of Gabidulin codes (original) (raw)

Abstract

Gabidulin codes are the analogues of Reed–Solomon codes in rank metric and play an important role in various applications. In this contribution, a method for efficient decoding of Gabidulin codes up to their error correcting capability is shown. The new decoding algorithm for Gabidulin codes (defined over \({\mathbb{F}_{q^m}}\)) directly provides the evaluation polynomial of the transmitted codeword. This approach can be seen as a Gao-like algorithm and uses an equivalent of the Euclidean Algorithm. In order to achieve low complexity, a fast symbolic product and a fast symbolic division are presented. The complexity of the whole decoding algorithm for Gabidulin codes is \({\mathcal{O} (m^3 \, \log \, m)}\) operations over the ground field \({\mathbb{F}_q}\) .

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Authors and Affiliations

  1. Institute of Communications Engineering, University of Ulm, Ulm, Germany
    Antonia Wachter-Zeh & Vladimir Sidorenko
  2. Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1, Rennes, France
    Antonia Wachter-Zeh
  3. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
    Valentin Afanassiev & Vladimir Sidorenko

Authors

  1. Antonia Wachter-Zeh
  2. Valentin Afanassiev
  3. Vladimir Sidorenko

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Correspondence toAntonia Wachter-Zeh.

Additional information

This contribution was presented in part at the Seventh International Workshop on Coding and Cryptography 2011 (WCC 2011), April 2011, Paris, France [23].

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

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Wachter-Zeh, A., Afanassiev, V. & Sidorenko, V. Fast decoding of Gabidulin codes.Des. Codes Cryptogr. 66, 57–73 (2013). https://doi.org/10.1007/s10623-012-9659-5

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