List Decoding of Lifted Gabidulin Codes via the Plücker Embedding

Codes in the Grassmannian have recently found an application in random network coding. All the codewords in such codes are subspaces of Fq with a given dimension. In this paper, we consider the problem of list decoding of a certain family of codes in the Grassmannian, called lifted Gabidulin codes. For this purpose we use the Plücker embedding of the Grassmannian. We describe a way of representing a subset of the Plücker coordinates of lifted Gabidulin codes as linear block codes. The union of the parity-check equations of these block codes and the equations which arise from the description of a ball around a subspace in the Plücker coordinates describe the list of codewords with distance less than a given parameter from the received word.