Reed-Solomon codes have found many applications in practical storage systems, but were until recently considered unsuitable for distributed storage applications due to the widely-held belief that they have poor repair bandwidth. 

Guruswami and Wootters (STOC'16) showed that one can actually perform bandwidth-efficient linear repair with Reed-Solomon codes: when the codes are over the field $GF(q^t)$ and the number of parities $r geq q^s$, where $(t-s) | t$, there exists a scheme that achieves a repair bandwidth of $(n-1)(t-s)log(q)$ bits, which is optimal among all linear repair schemes for Reed-Solomon codes when $n = q^t$ and $r = q^s$. We propose to use a linearized polynomial instead of the trace polynomial and are able to prove this result for every $s < t$. We also extend Guruswami-Wootters framework to tackle two or three erasures.