List Decoding of Lifted Gabidulin Codes via the Plücker Embedding
Anna-Lena Trautmann, Natalia Silberstein, Joachim Rosenthal · arXiv (Cornell University) · 2013
Codes in the Grassmannian have recently found an application in random network coding. All the codewords in such codes are subspaces of $\F_q^n$ 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.