多节点修复的代数几何码  

Repairing multiple failures for algebraic geometry codes

作　　者：胡万宝 胡帅 陈雯雯 崔良武 HU Wanbao;HU Shuai;CHEN Wenwen;CUI Liangwu(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《中国科学技术大学学报》2020年第2期140-145,共6页JUSTC

基　　金：国家自然科学基金(11601009)资助.

摘　　要：最小存储再生码的每个节点具有最小的数据存储,因而是最大距离可分码,这样其节点数的上界为2^(b),其中b是存储在每个节点中的数据的比特数.从理论和实践的角度来看,我们很自然地会去考虑这样的再生码:其具有接近最小的数据存储并且节点数不受此界的限制.针对这一问题,Jin等用代数几何码构造再生码,推广了Wotters和Guruswami的Reed-Solomon修复算法.本文在此基础上进行了扩展,给出了多节点修复的代数几何再生码.这推广和改进了最近一些关于再生码的结果,例如多失效节点的Reed-Solomon码和scalar MDS码.Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable codes.Thus,the number of nodes is upper-bounded by 2^(b),where b is the bits of data stored in each node.From both theoretical and practical points of view,it is natural to consider regenerating codes that nearly have minimum storage of data,and meanwhile,the number of nodes is unbounded.Aiming at the problem,Jin et al.constructed the regenerating codes by algebraic geometry codes,which generalized the repairing algorithm of Reed-Solomon codes by Guruswami and Wotters.This paper mainly gives a construction to repair multiple failures for algebraic geometry codes,which extends the framework of repairing one failure for the regenerating codes.The results generalize some quite recent results in which regenerating codes,for instance,Reed-Solomon codes and scalar codes with multiple erasures.

关 键 词：分布式存储系统 再生码 REED-SOLOMON码 代数几何码 带宽 

分 类 号：O157.4[理学—数学] TN911.22[理学—基础数学]