论文标题
用子包装构建MSR代码$ 2^{n/3} $ $ k+1 $ helper节点
Constructing MSR codes with subpacketization $2^{n/3}$ for $k+1$ helper nodes
论文作者
论文摘要
Wang等。 （信息理论的IEEE交易，第62卷，第8期，2016年）提出了$（n = k+2，k）的明确构造，$最低存储再生（MSR）代码（MSR）代码，带有$ 2 $ Parity Nodes和Subpacketization $ 2^{K/3} $。此代码的辅助节点的数量为$ d = k+1 = n-1 $，并且该代码在所有现有的MSR代码的现有显式构造中具有最小的子包装，并具有相同的$ n，k $和$ d $。在本文中，我们为更广泛的参数介绍了新的MSR码结构。更确切地说，我们仍然可以修复$ d = k+1 $，但是我们允许代码长度$ n $是满足$ n \ ge k+2 $的任何整数。代码的字段大小在$ n $中是线性的，我们代码的子包装为$ 2^{n/3} $。该值略大于Wang等人的构造的子包装。因为他们的代码构造仅保证所有系统节点的最佳维修，而我们的代码构造保证了所有节点的最佳维修。
Wang et al. (IEEE Transactions on Information Theory, vol. 62, no. 8, 2016) proposed an explicit construction of an $(n=k+2,k)$ Minimum Storage Regenerating (MSR) code with $2$ parity nodes and subpacketization $2^{k/3}$. The number of helper nodes for this code is $d=k+1=n-1$, and this code has the smallest subpacketization among all the existing explicit constructions of MSR codes with the same $n,k$ and $d$. In this paper, we present a new construction of MSR codes for a wider range of parameters. More precisely, we still fix $d=k+1$, but we allow the code length $n$ to be any integer satisfying $n\ge k+2$. The field size of our code is linear in $n$, and the subpacketization of our code is $2^{n/3}$. This value is slightly larger than the subpacketization of the construction by Wang et al. because their code construction only guarantees optimal repair for all the systematic nodes while our code construction guarantees optimal repair for all nodes.
