Constructions of Binary Locally Repairable Codes With Multiple Recovering Sets

Locally repairable codes (LRCs) with multiple recovering sets are highly demanded in distributed storage systems. In this letter, we generalize the construction of WZL code proposed by Wang et al. and give a construction of optimal binary LRCs with multiple disjoint recovering sets which can reach the upper bound on the code rate given by Kadhe et al.. Then we further generalize our idea to obtain a construction of binary LRCs with intersect recovering sets. The code rate is much higher than that of WZL code and is very closed to the construction of Kruglik et al. Moreover, two special cases of this construction can reach the upper bound on the minimum distance.