An Integer Programming-Based Bound for Locally Repairable Codes

doi:10.1109/TIT.2015.2472515

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	An Integer Programming-Based Bound for Locally Repairable Codes
	Wang, Anyu 1; Zhang, Zhifang2
	2015-10-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	61 期号:10 页码:5280-5294
摘要	The locally repairable code (LRC) studied in this paper is an right perpendicularn, kleft perpendicular linear code of which the value at each coordinate can be recovered by a linear combination of at most r other coordinates. The central problem in this paper is to determine the largest possible minimum distance for LRCs. First, an integer programming- based upper bound is derived for any LRC. Then, by solving the programming problem under certain conditions, an explicit upper bound is obtained for LRCs with parameters n(1) > n(2), where n(1) = right perpendicular(n/r + 1)left perpendicular and n(2) = n(1)(r+1)-n. Finally, an explicit construction for LRCs attaining this upper bound is presented over the finite field F(2)m, where m >= n(1)r. Based on these results, the largest possible minimum distance for all LRCs with r <= root n - 1 has been definitely determined, which is of great significance in practical use.
关键词	Distributed storage erasure codes locally repairable codes linear codes
DOI	10.1109/TIT.2015.2472515
语种	英语
资助项目	National Key Basic Research Project of China[2011CB302400] ; National Science Foundation of China[61379139] ; Strategic Priority Research Program through the Chinese Academy of Sciences[XDA06010701] ; National Natural Science Foundation of China[61121062/F02] ; 973 Project[2011CB302401]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000361486800004
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20762
专题	系统科学研究所
通讯作者	Wang, Anyu
作者单位	1.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China 2.Chinese Acad Sci, AMSS, NCMIS, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Anyu,Zhang, Zhifang. An Integer Programming-Based Bound for Locally Repairable Codes[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2015,61(10):5280-5294.
APA	Wang, Anyu,&Zhang, Zhifang.(2015).An Integer Programming-Based Bound for Locally Repairable Codes.IEEE TRANSACTIONS ON INFORMATION THEORY,61(10),5280-5294.
MLA	Wang, Anyu,et al."An Integer Programming-Based Bound for Locally Repairable Codes".IEEE TRANSACTIONS ON INFORMATION THEORY 61.10(2015):5280-5294.