New Constructions of Short Length Binary Locally Repairable Codes

In this short paper, our main objective is to construct binary locally repairable codes (LRCs) with good properties. Two constructions of LRCs with short lengthes are proposed. The first one is that define a u-linearly independent set (u-LIS) of an LRC with disjoint repair groups (DRGs) and enlarge it into another one with bigger size to construct new LRCs. The second is puncturing check matrices of known codes to construct new LRCs. As an application, many new binary LRCs are constructed from distance optimal linear codes, which are also locality optimal according to the Cadambe-Mazumdar (C-M) bound.