最优局部修复码研究综述  

A survey on optimal locally repairable codes

作　　者：马立明 邢朝平 Liming Ma;Chaoping Xing

机构地区：[1]中国科学技术大学数学学院,合肥230026 [2]上海交通大学电子信息与电气工程学院,上海200240

出　　处：《中国科学：数学》2021年第10期1495-1512,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12031011);华为-上海交大联合项目资助项目。

摘　　要：局部修复码或局部恢复码(locally repairable/recoverable codes, LRC)是为分布式存储系统和云存储系统的应用而设计的.与经典分组码相似,局部修复码也有一个重要的界,称为Singleton-型上界.在本文中,达到Singleton-型上界的分组码称为最优局部修复码.类似于经典的极大距离可分码(maximum distance separable codes, MDS码),最优局部修复码具有一些非常好的组合结构.自从引入局部修复码的Singleton-型上界后,人们在构造最优局部修复码方面做了很多有意义的工作.本文将综述性地介绍目前国际上关于最优局部修复码的若干界和构造方面的工作.Locally repairable codes, or locally recoverable codes(LRC for short) are designed for application in distributed and cloud storage systems. Similar to the classical block codes, there is an important bound called the Singleton-type bound for locally repairable codes. In this paper, an optimal locally repairable code refers to a block code achieving this Singleton-type bound. Like the classical MDS(maximum distance separable) codes,the optimal locally repairable codes have some very nice combinatorial structures. Since the introduction of Singleton-type bound for locally repairable codes, people have put tremendous effort on constructions of optimal locally repairable codes. In this paper, we give a survey on optimal locally repairable codes, including bounds and constructions.

关 键 词：局部修复码 函数域 线性码 校验矩阵 

分 类 号：O157.4[理学—数学] TP333[理学—基础数学]