论文标题
最佳本地维修代码：改进的绑定和构造
Optimal Locally Repairable Codes: An Improved Bound and Constructions
论文作者
论文摘要
我们研究单胎型结合，该结合提供了可局部可维修代码的最小距离的上限。通过仔细分析修复集的组合结构，我们提出了改进的约束。因此，我们显示了某些参数无法实现的先前界限。然后，我们还提供了最佳代码的明确结构，这些构造表明对于某些参数，新界限很清晰。此外，作为副产品，一些以前已知的代码被证明可以达到新的结合，因此被证明是最佳的。
We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes that show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.
