  A major issue of locally repairable codes is their robustness. If a local
repair group is not able to perform the repair process, this will result in
increasing the repair cost. Therefore, it is critical for a locally repairable
code to have multiple repair groups. In this paper we consider robust locally
repairable coding schemes which guarantee that there exist multiple distinct
(not necessarily disjoint) alternative local repair groups for any single
failure such that the failed node can still be repaired locally even if some of
the repair groups are not available. We use linear programming techniques to
establish upper bounds on the code size of these codes. We also provide two
examples of robust locally repairable codes that are optimal regarding our
linear programming bound. Furthermore, we address the update efficiency problem
of the distributed data storage networks. Any modification on the stored data
will result in updating the content of the storage nodes. Therefore, it is
essential to minimise the number of nodes which need to be updated by any
change in the stored data. We characterise the update-efficient storage code
properties and establish the necessary conditions of existence update-efficient
locally repairable storage codes.
