New Technique for Decoding Codes in the Rank Metric and Its Cryptography Applications
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A Fast Matrix Decoding Algorithm for Rank-Error-Correcting Codes
Proceedings of the First French-Soviet Workshop on Algebraic Coding
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Error and erasure correcting algorithms for rank codes
Designs, Codes and Cryptography
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Fast encoding and decoding of Gabidulin codes
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Fast decoding of Gabidulin codes
Designs, Codes and Cryptography
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Designs, Codes and Cryptography
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In this paper, we present a new approach of the decoding of Gabidulin codes. We show that, in the same way as decoding Reed-Solomon codes is an instance of the problem called polynomial reconstruction, the decoding of Gabidulin codes can be seen as an instance of the problem of reconstruction of linearized polynomials. This approach leads to the design of two efficient decoding algorithms inspired from the Welch–Berlekamp decoding algorithm for Reed–Solomon codes. The first algorithm has the same complexity as the existing ones, that is cubic in the number of errors, whereas the second has quadratic complexity in 2.5n2 – 1.5k2.