A Generic Transformation to Generate MDS Array Codes With δ-Optimal Access Property

Recently, some high-rate maximum distance separable (MDS) array codes were designed to optimally repair a single failed node by connecting all the surviving nodes. However, in practical systems, sometimes not all the surviving nodes are available. To facilitate the practical storage system, a few constructions of
$(n,k)$
MDS array codes with the property that any single failed node can be optimally repaired by accessing any
$d$
surviving nodes (i.e., minimum-storage regenerating (MSR) codes) have been proposed, where
$d\in [k+1:n-1)$
. However, all high-rate MDS array codes with this property either have large sub-packetization levels or are not explicit for all the parameters. To address these issues, we propose a generic transformation that can convert any
$(n',k')$
MDS array/scalar code to another
$(n=n'-\delta,k=k'-\delta)$
MDS array code with the optimal repair property and optimal access property for an arbitrary set of two nodes, while the repair efficiency of the remaining
$n-2$
nodes can be kept, where
$2\le \delta \le n'-k'$
. By recursively applying the generic transformation to an MDS scalar code multiple times, we get a high-rate MDS array code with the optimal repair property and the optimal access property for all nodes, which outperforms previous known high-rate MDS array codes in terms of either the sub-packetization level or the flexibility of the parameters.