Construction of Optimal Locally Repairable Codes of Triangular Association Schemes

As a new erasure code for distributed storage systems, locally repairable codes (LRCs) can effectively realize the reliable and efficient storage of massive data. The construction of locally repairable codes with (r,t) locality has become a research hotspot recently. Therefore, the construction methods of locally repairable codes based on triangular association schemes are proposed, which can construct optimal binary locally repairable codes with arbitrary (r,t) locality. Performance analyses show that the LRCs constructed with availability t=2 reach the optimal code rate bound, the LRCs constructed with arbitrary locality r>2 and availability t>2 reach the optimal minimum distance bound. The LRC constructed in this paper performs better in terms of code rate and more flexible parameter selection than those constructed based on near-regular graphs and direct product codes, etc.