New Binary Locally Repairable Codes with Locality 2 and Uneven Availabilities for Hot Data

In this paper, a new family of binary LRCs (BLRCs) with locality 2 and uneven availabilities for hot data is proposed, which has a high information symbol availability and low parity symbol availabilities for the local repair of distributed storage systems. The local repair of each information symbol for the proposed codes can be done not by accessing other information symbols but only by accessing parity symbols. The proposed BLRCs with k = 4 achieve the optimality on the information length for their given code length, minimum Hamming distance, locality, and availability in terms of the well-known theoretical upper bound