# 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
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#### References

SHOWING 1-10 OF 84 REFERENCES
Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm
• Mathematics, Computer Science
• Electron. Notes Discret. Math.
• 2017
Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding
• Mathematics, Computer Science
• 2015
Algebraic list-decoding of subspace codes with multiplicities
• Mathematics, Computer Science
• 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
• 2011
List-decoding of subspace codes and rank-metric codes up to Singleton bound
• Hessam Mahdavifar
• Computer Science, Mathematics
• 2012 IEEE International Symposium on Information Theory Proceedings
• 2012
Algebraic List-Decoding of Subspace Codes
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2013
Explicit rank-metric codes list-decodable with optimal redundancy
• Mathematics, Computer Science
• Electron. Colloquium Comput. Complex.
• 2013