Decoding interleaved Gabidulin codes and multisequence linearized shift-register synthesis

An interleaved Gabidulin code is the direct sum of ℓ Gabidulin codes. We propose an efficient decoding algorithm that corrects with high probability errors of rank up to (ℓ/ℓ+1)(d-1), where d is the rank distance of the interleaved code. The probability of decoding failure is estimated. The proposed decoding is based on a multisequence linearized shift-register synthesis algorithm, given in the paper. The time complexity of the decoding algorithm is O(ℓd²).