  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.
