In distributed storage systems, node erasures may occur frequently. An \((n,k,\ell )\) minimum storage regenerating (MSR) code provides the optimal-bandwidth repair of single node erasure whiling retaining the minimum storage overhead. For multi-node repair, centralized MSR and cooperative MSR codes are proposed to repair \(h\ge 2\) node erasures using d helper nodes in a centralized and cooperative way, respectively. \(\ell \) is called the sub-packetization of the code and d is called repair degree. In a remarkable work, Ye presented cooperative MSR codes (called Ye’s code) with sub-packetization \(\mathrm{{exp}}(O(n))\) by repeating a previous MSR code for \(d-k+h\) times. In this paper, motivated by Ye’s code, we find observations to build new centralized multi-node repair schemes of codes with small sub-packetization. The first code is designed for a single pair of (h, d) and the second code is for all possible pairs of (h, d) simultaneously. The main technique adopts a generalized space-sharing method and modifies Ye’s code to get new centralized repair schemes with less space-sharing. The resultant code has sub-packetization no more than \(\mathrm{{lcm}}(1,2,\ldots ,n-k)(n-k)^n\) , which is much smaller than a previous work given by Ye and barg ( \((\mathrm{{lcm}}(1,2,\ldots ,n-k))^n\) ).
