构造小域上的最优局部修复码  

Constructions of optimal locally repairable codes over small fields

作　　者：张志芳[1] 徐敬可 刘木兰[1] 

机构地区：[1]中国科学院数学与系统科学研究院,北京100190

出　　处：《中国科学：数学》2017年第11期1607-1614,共8页Scientia Sinica：Mathematica

摘　　要：局部修复码是近几年分布式存储编码领域一个非常热门的研究方向.满足局部修复性r即要求码字的一位能够被其他至多r位恢复.这种性质对于提高分布式存储系统中失效节点的修复效率非常重要.本文主要考虑了域规模小于n时最优局部修复码的构造.具体地,本文构造了有限域F_q(q=r/(r+1)n_1)满足所有位局部修复性r=2、d=6和d=r+1的最优局部修复码.Locally repairable codes is an attractive research object in recent years. A code coordinate has locality r if the value of this coordinate can be recovered as a function of the values of at most r other coordinates.This is an importaat property for reducing the repair complexity in distributed storage systems. In this paper, we consider the constructions of optimal locally repairable codes over finite fields with size smaller than the code ~rn length n. Specifically, over the finite field IFq with q=r/r＋l n＋1, we construct two classes of optimal locally repairable codes with r= 2, d = 6 and d = r ＋ 1 respectively.

关 键 词：局部修复码 最优极小距离 分布式存储系统 

分 类 号：O157.4[理学—数学]