Locality of optimal binary codes |
| |
Institution: | College of Science, Air Force Engineering University, Xi''an, Shaanxi 710051, PR China |
| |
Abstract: | The locality of locally repairable codes (LRCs) for a distributed storage system is the number of nodes that participate in the repair of failed nodes, which characterizes the repair cost. In this paper, we first determine the locality of MacDonald codes, then propose three constructions of LRCs with . Based on these results, for and , we give an optimal linear code with small locality. The distance optimality of these linear codes can be judged by the codetable of M. Grassl for and by the Griesmer bound for . Almost all the codes () have locality except for the three codes, and most of the code with achieves the Cadambe–Mazumdar bound for LRCs. |
| |
Keywords: | Locally repairable code Repair locality MacDonald code Optimal code |
本文献已被 ScienceDirect 等数据库收录! |
|