Linear programming bounds for robust locally repairable storage codes

Locally repairable codes are used in distributed storage networks to minimise the number of survived nodes required to repair a failed node. However, the robustness of these codes is a main concern since locally repair procedure may fail when there are multiple node failures. This paper proposes a new class of robust locally repairable codes which guarantees that a failed node can be repaired locally even when there are multiple node failures. Upper bound on the size of robust locally repairable codes using linear programming tools are obtained and examples of robust locally repairable codes attaining these bounds are constructed.