Optimal Locally Repairable Codes for Parallel Reading

Locally repairable codes (LRCs) have important applications in distributed storage systems. In this paper, we study q-ary [n; k; d] LRCs with (r; t; delta)-information-locality, where each of the i-th (1 <= i <= k) information symbol is contained in t punctured subcodes with length <= r + delta - 1, minimum distance delta, and the i-th information symbol is the unique common code symbol of these t subcodes, furthermore, each subcode contains exactly delta - 1 parity symbols. Firstly, an upper bound on the minimum distance of such q-ary LRCs with (r; t; delta)-information-locality is given. Then, we propose a general construction framework of q-ary optimal LRCs with (r; t; delta)-information-locality and minimum distance d D t(delta - 1) + 1 where the required field size is just q >= r + delta-2 The proposed optimal LRCs can always repair a failed information node locally in case of at most t delta - 1 node failures. Moreover, multiple repair subcodes can support parallel readings of data, thus make the proposed codes attractive for distributed storage systems with hot data.