New constructions of binary MDS array codes and locally repairable array codes

In this paper, we firstly present a new construction of binary maximum distance separable (MDS) array codes, from which some types of new MDS array codes of minimum distance 4 with array dimension (p−1)×(ℓ+2) can be deduced. Based on the construction, binary locally repairable array codes (LRACs) of minimum distance 4 are also explored, whose array dimension is (p−1)×2ℓ and column locality is ℓ − 1. Particularly, when 2 is a primitive root module p, a scheduled algorithm for syndrome computation of the LRACs is proposed, which converges to 2 XORs per data bit when ℓ approaches infinity.