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Coding for distributed storage gives rise to a new set of problems in codingtheory related to the need of reducing inter-node communication in the system.A large number of recent papers addressed the problem of optimizing the totalamount of information downloaded for repair of a single failed node (the repairbandwidth) by accessing information on $d$ {\em helper nodes}, where $k\le d\len-1.$ By the so-called cut-set bound (Dimakis et al., 2010), the repairbandwidth of an $(n,k=n-r)$ MDS code using $d$ helper nodes is at least$dl/(d+1-k),$ where $l$ is the size of the node. Also, a number of knownconstructions of MDS array codes meet this bound with equality. In a relatedbut separate line of work, Guruswami and Wootters (2016) studied repair ofReed-Solomon (RS) codes, showing that these codes can be repaired using asmaller bandwidth than under the trivial approach. At the same time, their workas well as follow-up papers stopped short of constructing RS codes (or anyscalar MDS codes) that meet the cut-set bound with equality, which has been anopen problem in coding theory. In this work we present a solution to thisproblem, constructing RS codes of length $n$ over the field $q^l,l=\exp((1+o(1))n\log n)$ that meet the cut-set bound. We also prove an almostmatching lower bound on $l$, showing that the super-exponential scaling is bothnecessary and sufficient for achieving the cut-set bound using linear repairschemes. More precisely, we prove that for scalar MDS codes (including the RScodes) to meet this bound, the sub-packetization $l$ must satisfy $l \ge\exp((1+o(1)) k\log k).$

Optimal repair of Reed-Solomon codes: Achieving the cut-set bound