Repair Optimal Erasure Codes Through Hadamard Designs

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In distributed storage systems that employ erasure coding, the issue of minimizing the total communication required to exactly rebuild a storage node after a failure arises. This repair bandwidth depends on the structure of the storage code and the repair strategies used to restore the lost data. Designing high-rate Maximum-Distance Separable (MDS) codes that achieve the optimum repair communication has been a well-known open problem. In this paper, the authors use Hadamard matrices to construct the first explicit 2-parity MDS storage code with optimal repair properties for all single node failures, including the parities.