On transform – domain decoding of Gabidulin codes

Gabidulin codes are the rank metric analogues of Reed–Solomon codes and found many applications including network coding. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. In this paper, for Gabidulin codes we propose a transform–domain algorithm correcting both errors and erasures. We show how to generalize this algorithm for interleaved Gabidulin codes. The transform–domain approach allows to simplify derivations and proofs and also simplifies finding the error vector after solving the key equation.

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