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Recently, locally repairable codes has gained significant interest for theirpotential applications in distributed storage systems. However, mostconstructions in existence are over fields with size that grows with the numberof servers, which makes the systems computationally expensive and difficult tomaintain. Here, we study linear locally repairable codes over the binary field,tolerating multiple local erasures. We derive bounds on the minimum distance onsuch codes, and give examples of LRCs achieving these bounds. Our maintechnical tools come from matroid theory, and as a byproduct of our proofs, weshow that the lattice of cyclic flats of a simple binary matroid is atomic.

Bounds on Binary Locally Repairable Codes Tolerating Multiple Erasures