Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771570 | Finite Fields and Their Applications | 2017 | 24 Pages |
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 r=1,2 and 3. Based on these results, for 2â¤kâ¤7 and nâ¥k+2, we give an optimal linear [n,k,d] code with small locality. The distance optimality of these linear codes can be judged by the codetable of M. Grassl for n<2(2kâ1) and by the Griesmer bound for nâ¥2(2kâ1). Almost all the [n,k,d] codes (2â¤kâ¤7) have locality râ¤3 except for the three codes, and most of the [n,k,d] code with n<2(2kâ1) achieves the Cadambe-Mazumdar bound for LRCs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Qiang Fu, Ruihu Li, Luobin Guo, Liangdong Lv,