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In the literature, most of the known high-rate $(n,k)$ MDS array codes withthe optimal repair property only support a single repair degree (i.e., thenumber of helper nodes contacted during a repair process) $d$, where $k\le d\len-1$. However, in practical storage systems, the number of available nodeschanges frequently. Thus, it is preferred to construct $(n,k)$ MDS array codeswith multiple repair degrees and the optimal repair property for all nodes. Tothe best of our knowledge, only two MDS array codes have such properties in theliterature, which were proposed by Ye and Barg (IEEE Trans. Inform. Theory,63(10), 2001-2014, 2017). However, their sub-packetization levels arerelatively large. In this paper, we present a generic construction method thatcan convert some MDS array codes with a single repair degree into the ones withmultiple repair degrees and optimal repair property for a set of nodes, whilethe repair efficiency/degrees of the remaining nodes can be kept. As anapplication of the generic construction method, an explicit construction ofhigh-rate MDS array code with multiple repair degrees and the optimal accessproperty for all nodes is obtained over a small finite field. Especially, thesub-packetization level is much smaller than that of the two codes proposed byYe and Barg concerning the same parameters $n$ and $k$.

Optimal Repair/Access MDS Array Codes with Multiple Repair Degrees