  Despite their exceptional error-correcting properties, Reed-Solomon codes
have been overlooked in distributed storage applications due to the common
belief that they have poor repair bandwidth: A naive repair approach would
require the whole file to be reconstructed in order to recover a single erased
codeword symbol. In a recent work, Guruswami and Wootters (STOC'16) proposed a
single-erasure repair method for Reed-Solomon codes that achieves the optimal
repair bandwidth amongst all linear encoding schemes. Their key idea is to
recover the erased symbol by collecting a sufficiently large number of its
traces, each of which can be constructed from a number of traces of other
symbols. We extend the trace collection technique to cope with two and three
erasures.
