Construction of Optimal Locally Repairable Codes Based on RBIBD

With the rapid growth of data, the requirements of the reliability and effectiveness for distributed storage systems are increasing. Locally repairable codes (LRCs) have better locality, which can effectively realize the reliable and efficient storage of massive data in distributed storage system. It has become a research hotspot to construct locally repairable codes with (r, t) locality. Therefore, this paper proposes a construction method of optimal locally repairable codes based on resolvable balanced incomplete block design (RBIBD), which can construct binary optimal single parity LRCs with (r, t) locality of information symbols. The performance analyses show that, the constructed LRCs reach the minimum distance bound, and compared with the LRCs proposed by Xia et al., the LRCs proposed in this paper perform better in code rate. In particular, when the availability t=2, the LRCs is also the code with the optimal code rate.