This paper proposes to construct binary array codes from nonbinary codes by binary matrix dispersion. Thanks to their low-density and quasi-cyclic generator matrices, thesebinary dispersed array codes(BDACs) enjoy low encoding complexity. Their reconstruction property is characterized through matrix transformation. Several explicit constructions of BDACs from minimum-bandwidth regenerating codes, piggybacking codes, and locally recoverable codes are presented, as well as their similar single-node repair strategies to their nonbinary counterparts.

This paper proposes to construct binary array codes from non-binary codes by binary matrix dispersion. Thanks to their low-density and quasi-cyclic (QC) generator matrices, the proposed codes enjoy low encoding complexity, about$1/(m+1)$of the XOR operations used in their counterparts over$\mathbf{G F}\left(2^m\right)$. Their maximum distance separable (MDS) property and repair can be efficiently analyzed via matrix transformation. The MDS property is ensured by introducing Vandermonde upper triangular form and pre-processing. Moreover, the efficient repair can be guaranteed by applying a matrix mapping called all-one superposition on the associated matrices. Analysis indicates that their code rate and repair ratio asymptotically approach those of their non-binary counterparts.

This paper considers the parity-check matrix of a maximum distance separable (MDS) array code as a superposition of two matrices, block diagonal matrix A and side matrix S. By matching their entries, the syndrome calculation of the matrix A can share computations with that of the side matrix S. Then, a low-complexity encoding, referred to as side encoding, is proposed to encode matched MDS array codes efficiently. Moreover, it can combine with the Reed-Muller transform-based (RMTB) Reed-Solomon encoding algorithm to reduce the encoding complexity further. The analysis indicates that for the MDS array code [1] with four parity nodes, the number of multiplications is reduced by 85.4% and 52.6% compared to the traditional encoding and only RMTB encoding, respectively.