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An Integer Programming-Based Bound for Locally Repairable Codes
Wang, Anyu1; Zhang, Zhifang2
AbstractThe 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.
KeywordDistributed storage erasure codes locally repairable codes linear codes
Funding ProjectNational 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 Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000361486800004
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Document Type期刊论文
Corresponding AuthorWang, Anyu
Affiliation1.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
Recommended Citation
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.
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