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On the SingleParity Locally Repairable Codes
Yanbo LU Jie HAO ShuTao XIA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E100A
No.6
pp.13421345 Publication Date: 2017/06/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E100.A.1342 Type of Manuscript: LETTER Category: Coding Theory Keyword: linear codes, erasure codes, code locality, locally repairable codes, distance bounds,
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Summary:
Locally repairable codes (LRCs) have attracted much interest recently due to their applications in distributed storage systems. In an [n,k,d] linear code, a code symbol is said to have locality r if it can be repaired by accessing at most r other code symbols. An (n,k,r) LRC with locality r for the information symbols has minimum distance d≤nk⌈k/r⌉+2. In this letter, we study singleparity LRCs where every repair group contains exactly one parity symbol. Firstly, we give a new characterization of singleparity LRCs based on the standard form of generator matrices. For the optimal singleparity LRCs meeting the Singletonlike bound, we give necessary conditions on the structures of generator matrices. Then we construct all the optimal binary singleparity LRCs meeting the Singletonlike bound d≤nk⌈k/r⌉+2.

