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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. The work of Guruswami and Wootters (STOC'16) has shown that one can actually perform bandwidth-efficient linear repair with Reed-Solomon codes: When the codes are over the field Fqt and the number of parities r &#x2265; qs, where (t - s) divides t, there exists a linear scheme that achieves a repair bandwidth of (n - 1)(t - s) logg q bits. We extend this result by showing the existence of such a linear repair scheme for every 1 &#x2264; s &lt;; t. Moreover, our new schemes are optimal among all linear repair schemes for Reed-Solomon codes when n = qt and r = qs. Additionally, we improve the lower bound on the repair bandwidth for Reed-Solomon codes, also established in the work of Guruswami and Wootters.

Optimal repair schemes for some families of full-length reed-solomon codes