Fast decoding of Gabidulin codes
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 ) 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 operations over the ground field F-q.
fast decoding gabidulin codes rank metric fast symbolic product fast symbolic division linearized polynomials