Date of Original Version
© ACM, 2012. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published at http://doi.acm.org/10.1145/2090236.2090252
Abstract or Description
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our construction is based on a variant of the folded Reed-Solomon codes in the world of linearized polynomials, and the algorithm is inspired by the recent linear-algebraic approach to list decoding. Ours is the first list decoding algorithm for subspace codes that can handle deletions; even one deletion can totally distort the structure of the basis of a subspace and is thus challenging to handle. When there are only insertions, we also present results for list decoding subspace codes that are the linearized analog of Reed-Solomon codes (proposed previously, and closely related to the Gabidulin codes for rank-metric), obtaining some improvements over similar results in previous work.
Proceedings of the Conference on Innovations in Theoretical Computer Science (ITCS), 2012, 183-189.