Constructions of optimal binary locally repairable codes via intersection subspaces

Abstract

Locally repairable codes (LRCs), which can recover any symbol of a codeword by reading only a small number of other symbols, have been widely used in real-world distributed storage systems, such as Microsoft Azure Storage and Ceph Storage Cluster. Since binary linear LRCs can significantly reduce coding and decoding complexity, constructions of binary LRCs are of particular interest. The aim of this paper is to construct dimensional optimal binary LRCs with disjoint local repair groups. We introduce a method to connect intersection subspaces with binary LRCs and construct dimensional optimal binary linear LRCs with locality 2^b (b ≽ 3) and minimum distance d ≽ 6 by employing intersection subspaces deduced from the direct sum. This method will sufficiently increase the number of possible repair groups of dimensional optimal LRCs, thus efficiently expanding the range of the construction parameters while keeping the largest code rates compared with all known binary linear LRCs with minimum distance d ≽ 6 and locality 2^b.