Repairing Reed-Solomon Codes via Subspace Polynomials

We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature employ trace polynomials. The are over \mathbb F ql have redundancy r = n-k ≥ q m , 1 ≤ m l where n k code length dimension, respectively. In particular, one erasure, we show our can achieve optimal bandwidths whenever n=q xmlns:xlink="http://www.w3.org/1999/xlink">l all . For two erasures, same bandwidth per erasure as single schemes, /m is a power of q, xmlns:xlink="http://www.w3.org/1999/xlink">a m=q xmlns:xlink="http://www.w3.org/1999/xlink">b -1 > ( b 1), /2 when even two.