Row reduction applied to decoding of rank-metric and subspace codes

@article{Puchinger2017RowRA,
  title={Row reduction applied to decoding of rank-metric and subspace codes},
  author={S. Puchinger and Johan Rosenkilde n'e Nielsen and Wenhui Li and V. Sidorenko},
  journal={Designs, Codes and Cryptography},
  year={2017},
  volume={82},
  pages={389-409}
}
We show that decoding of $$\ell $$ℓ-Interleaved Gabidulin codes, as well as list-$$\ell $$ℓ decoding of Mahdavifar–Vardy (MV) codes can be performed by row reducing skew polynomial matrices. Inspired by row reduction of $$\mathbb {F}[x]$$F[x] matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into a certain reduced form. We apply this to solve generalised shift register problems over skew polynomial rings which occur in decoding $$\ell… Expand
Fast Root Finding for Interpolation-Based Decoding of Interleaved Gabidulin Codes
Decoding High-Order Interleaved Rank-Metric Codes
Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm
Rank-Metric Codes Over Finite Principal Ideal Rings and Applications
The State of Lexicodes and Ferrers Diagram Rank-Metric Codes
On interleaved rank metric codes
Maximal Ferrers Diagram Codes: Constructions and Genericity Considerations
Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric

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