A Generic Transformation for Optimal Repair Bandwidth and Rebuilding Access in MDS Codes

We propose a generic transformation on maximum distance separable (MDS) codes, which can convert any non-binary (k+r, k) MDS code into another (k+r, k) MDS code with the following properties: 1) An arbitrarily chosen r nodes will have the optimal repair bandwidth and the optimal rebuilding access, 2) the repair bandwidth and rebuilding access efficiencies of all other nodes are maintained as in the code before the transformation, 3) it uses the same finite field as the code before the transformation, and 4) the sub-packetization is increased only by a factor of r. As two immediate applications of this powerful transformation, we show that 1) any non-binary MDS code with optimal repair bandwidth, or optimal rebuilding access, for only systematic nodes can be converted into an MDS code with the corresponding repair optimality for all nodes; and 2) any non-binary scalar MDS code can be converted to an MDS code with optimal repair bandwidth and rebuilding access for all nodes, or to an MDS code with optimal rebuilding access for all systematic nodes and moreover with the optimal sub-packatization, by applying the transformation multiple times.