A Fast Matrix Decoding Algorithm for Rank-Error-Correcting Codes
Proceedings of the First French-Soviet Workshop on Algebraic Coding
Probabilistic algorithm for finding roots of linearized polynomials
Designs, Codes and Cryptography
Fast encoding and decoding of Gabidulin codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
A welch–berlekamp like algorithm for decoding gabidulin codes
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Maximum-rank array codes and their application to crisscross error correction
IEEE Transactions on Information Theory
Coding for Errors and Erasures in Random Network Coding
IEEE Transactions on Information Theory
A Rank-Metric Approach to Error Control in Random Network Coding
IEEE Transactions on Information Theory
Linearized Shift-Register Synthesis
IEEE Transactions on Information Theory
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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 $${\mathbb{F}_q}$$ .