Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 547–567 | Cite as

Improved syndrome decoding of lifted \(L\)-interleaved Gabidulin codes

  • Hannes BartzEmail author
  • Vladimir Sidorenko
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography


A syndrome decoding algorithm for lifted interleaved Gabidulin codes of order L is proposed. The algorithm corrects L times more deviations (packet insertions) than known syndrome decoding methods with probability at least \(1-8q^{-n}\), where n is the length of the (interleaved) Gabidulin code. For \(n<L\), the proposed scheme has L times less computational complexity than known interpolation-factorization based decoders which attain the same decoding region. Upper bounds on the decoding failure probability are derived. Up to our knowledge this is the first syndrome-based scheme for interleaved subspace codes that can correct deviations beyond the unique decoding radius.


Subspace codes Rank-metric codes Interleaved Gabidulin codes Probabilistic unique decoding Syndrome-based decoding 

Mathematics Subject Classification

Primary 94B35 94B05 



The authors would like to thank Manuela Meier for developing the simulation framework for the improved syndrome decoder.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Communications and NavigationGerman Aerospace Center (DLR)OberpfaffenhofenGermany
  2. 2.Institute for Communications EngineeringTechnical University of Munich (TUM)MunichGermany

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