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In this paper, the authors present a new explicit construction for Locally Repairable Codes (LRCs) for distributed storage systems. The codes possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number of node failures. This construction, based on Maximum Rank Distance (MRD) Gabidulin codes, provides minimum distance optimal vector and scalar LRCs for a wide range of parameters. In addition, vector LRCs that allow for efficient local repair of failed nodes are considered. Towards this, the paper derives an upper bound on the amount of data that can be stored on DSS employing minimum distance optimal LRCs with given repair bandwidth, and presents codes which attain this bound by combining MRD and Minimum Storage Regenerating (MSR) codes.
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