  We show how Gabidulin codes can be decoded via parametrization by using
interpolation modules over the ring of linearized polynomials with composition.
Our decoding algorithm computes a list of message words that correspond to all
closest codewords to a given received word. This involves the computation of a
minimal basis for the interpolation module that corresponds to the received
word, followed by a search through the parametrization for valid message words.
Our module-theoretic approach strengthens the link between Gabidulin decoding
and Reed-Solomon decoding. Two subalgorithms are presented to compute the
minimal basis, one iterative, the other an extended Euclidean algorithm. Both
of these subalgorithms have polynomial time complexity. The complexity order of
the overall algorithm, using the parametrization, is then compared to
straightforward exhaustive search as well as to chase list decoding.
