Cooperative MSR codes are a kind of storage codes which enable optimal-bandwidth repair of any $h\geq2$ node erasures in a cooperative way, while retaining the minimum storage as an $[n,k]$ MDS code. Each code coordinate (node) is assumed to store an array of $\ell$ symbols, where $\ell$ is termed as sub-packetization. Large sub-packetization tends to induce high complexity, large input/output in practice. To address the disk IO capability, a cooperative MSR code is said to have optimal-access property, if during node repair, the amount of data accessed at each helper node meets a theoretical lower bound. In this paper, we focus on reducing the sub-packetization of optimal-access cooperative MSR codes with two erasures. At first, we design two crucial MDS array codes for repairing a specific repair pattern of two erasures with optimal access. Then, using the two codes as building blocks and by stacking up of the two codes for several times, we obtain an optimal-access cooperative MSR code with two erasures. The derived code has sub-packetization $\ell=r^{\binom{n}{2}-\lfloor\frac{n}{r}\rfloor(\binom{r}{2}-1)}$ where $r=n-k$, and it reduces $\ell$ by a fraction of $1/r^{\lfloor\frac{n}{r}\rfloor(\binom{r}{2}-1)}$ compared with the state of the art ($\ell=r^{\binom{n}{2}}$).

翻译：协作MSR码是一类存储编码，能够以协作方式对任意$h\geq2$个节点擦除实现最优带宽修复，同时保持作为$[n,k]$ MDS码的最小存储特性。每个码坐标（节点）被假定存储$\ell$个符号的数组，其中$\ell$被称为子分组化。较大的子分组化在实践中往往导致高复杂度和大规模输入/输出。为应对磁盘IO能力，若在节点修复过程中，每个辅助节点访问的数据量达到理论下界，则称该协作MSR码具有最优访问特性。本文聚焦于降低具有两个擦除的最优访问协作MSR码的子分组化水平。首先，我们针对特定双擦除修复模式设计了两类具有最优访问特性的关键MDS阵列码。随后，以这两类码为构建模块，通过多次堆叠组合，我们得到了具有两个擦除的最优访问协作MSR码。所推导的码具有子分组化$\ell=r^{\binom{n}{2}-\lfloor\frac{n}{r}\rfloor(\binom{r}{2}-1)}$，其中$r=n-k$。与现有最优结果（$\ell=r^{\binom{n}{2}}$）相比，该码将$\ell$降低了$1/r^{\lfloor\frac{n}{r}\rfloor(\binom{r}{2}-1)}$的比例。