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On the Single-Parity Locally Repairable Codes
Yanbo LU Jie HAO Shu-Tao XIA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2017/06/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Coding Theory
linear codes, erasure codes, code locality, locally repairable codes, distance bounds,
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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≤n-k-⌈k/r⌉+2. In this letter, we study single-parity LRCs where every repair group contains exactly one parity symbol. Firstly, we give a new characterization of single-parity LRCs based on the standard form of generator matrices. For the optimal single-parity LRCs meeting the Singleton-like bound, we give necessary conditions on the structures of generator matrices. Then we construct all the optimal binary single-parity LRCs meeting the Singleton-like bound d≤n-k-⌈k/r⌉+2.