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In modern practical data centers, storage nodes are usually organized intoequally sized groups, which is called racks. The cost of cross-rackcommunication is much more expensive compared with the intra-rack communicationcost. The codes for this system are called rack-aware regenerating codes.Similar to standard minimum storage regenerating (MSR) codes, it is achallenging task to construct minimum storage rack-aware regenerating (MSRR)codes achieving the cut-set bound. The known constructions of MSRR codesachieving the cut-set bound give codes with alphabet size $q$ exponential inthe code length $n$, more precisely, $q=\Omega(\exp(n^n))$.  The main contribution of this paper is to provide explicit construction ofMSRR codes achieving the cut-set bound with the alphabet size linear in $n$. Toachieve this goal, we first present a general framework to repair Reed-Solomoncodes. It turns out that the known repairing schemes of Reed-Solomon codes canbe realized under our general framework. Several techniques are used in thispaper. In particular, we use the degree decent method to repair failure node.This technique allows us to get Reed-Solomon codes with the alphabet sizelinear in $n$. The other techniques include choice of good polynomials. Notethat good polynomials are used for construction of locally repairable code inliterature. To the best of our knowledge, it is the first time in this paper tomake use of good polynomials for constructions of regenerating codes.

Optimal repairing schemes for Reed-Solomon codes with alphabet sizes linear in lengths under the rack-aware model