论文标题
最低距离$ 7 $的本地可维修代码的一些结果$ 2 $
Some results on locally repairable codes with minimum distance $7$ and locality $2$
论文作者
论文摘要
本地维修代码（LRC）在分布式存储系统（DSS）中起重要作用。 LRC较小的LRC具有自己的优势，因为在恢复删除的符号中需要更少的可用符号。在本文中，我们证明了最小距离$ d \ geq 7 $的LRC尺寸的上限。 $ d = 7 $，$ r = 2 $ at $ q^2+q+3 $的几乎最佳LRC的上限。 Then based on the $t$-spread structure, we give an algorithm to construct almost optimal LRCs with $d=7$, $r=2$ and length $n\geq 3\lceil\frac{\sqrt{2}q}{3}\rceil$ when $q\geq 4$, whose dimension attains the aforementioned upper bound.
Locally repairable codes(LRCs) play important roles in distributed storage systems(DSS). LRCs with small locality have their own advantages since fewer available symbols are needed in the recovery of erased symbols. In this paper, we prove an upper bound on the dimension of LRCs with minimum distance $d\geq 7$. An upper bound on the length of almost optimal LRCs with $d=7$, $r=2$ at $q^2+q+3$ is proved. Then based on the $t$-spread structure, we give an algorithm to construct almost optimal LRCs with $d=7$, $r=2$ and length $n\geq 3\lceil\frac{\sqrt{2}q}{3}\rceil$ when $q\geq 4$, whose dimension attains the aforementioned upper bound.
