New constructions of binary MDS array codes and locally repairable array codes
2022 IEEE International Symposium on Information Theory (ISIT), 2022•ieeexplore.ieee.org
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 …
(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 …
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.
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