On transform-domain error and erasure correction by Gabidulin codes

Gabidulin codes are the rank metric analogues of Reed–Solomon codes and have found many applications including network coding. In this paper, we propose a transform-domain algorithm correcting both errors and erasures with Gabidulin codes. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. We generalize the proposed decoding 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.