A Generic Transformation to Generate MDS Storage Codes with $δ$-Optimal Access Property

For high-rate maximum distance separable (MDS) codes, most of them are 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 codes with the property that any single failed node can be optimally repaired by accessing any $d$ surviving nodes have been proposed, where $d\in [k+1:n-1)$. However, all of them 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 code to another $(n,k)$ MDS 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. By recursively applying the generic transformation to a scalar MDS code multiple times, we get an MDS code with the optimal repair property and the optimal access property for all nodes, which outperforms previous known MDS codes in terms of either the sub-packetization level or the flexibility of the parameters.