Petabyte-scale distributed storage systems are currently transitioning to
erasure codes to achieve higher storage efficiency.
Locally Repairable Codes (LRCs) form a new family of codes that are repair
efficient. In particular, LRCs minimize the number of nodes participating in
single node repairs and provide simple and efficient codes that can be used in
practical systems.

The fundamental bounds for LRCs, namely the best possible distance for a given
code locality are known, but few explicit constructions exist. These prior
constructions are only valid for certain code parameters. In this work, we
present the first explicit construction of optimal Locally Repairable Codes, for
almost all possible parameter values. Moreover, we derive a new result in
Matroid theory for code analysis.