Balanced locally repairable codes

We introduce a family of balanced locally repairable codes (BLRCs) [n, k, d] for arbitrary values of n, k and d. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low repair locality. The novelty that we introduce in our construction is that we relax the strict requirement the repair locality to be a fixed small number l, and we allow the repair locality to be either l or l + 1. This gives us the flexibility to construct BLRCs for arbitrary values of n and k which partially solves the open problem of finding a general construction of LRCs. Additionally, the relaxed locality criteria gives us an opportunity to search for BLRCs that have a low repair locality even when double failures occur. We use metrics such as a storage overhead, an average repair bandwidth, a Mean Time To Data Loss (MTTDL) and an update complexity to compare the performance of BLRCs with existing LRCs.