An Improved Bound for Optimal Locally Repairable Codes

The Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes is studied. An improved bound is presented by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.