Lowest Density MDS Array Codes of Distance 3

We present a new family of maximum-distance separable (MDS) array codes of distance 3, called S(ymmetry)-Code, which has the properties of: 1) optimality in encoding, decoding and update; 2) code length of either p or p - 1 with p being an odd prime; 3) requiring less I/O cost than most existing lowest density MDS array codes during single-erasure recovery; and 4) approaching the lower bound in I/O cost of single-erasure recovery when the code length is small.