On the Single-Parity Locally Repairable Codes

Yanbo LU; Jie HAO; Shu-Tao XIA

doi:10.1587/transfun.E100.A.1342

On the Single-Parity Locally Repairable Codes

Yanbo LU, Jie HAO, Shu-Tao XIA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.6 pp.1342-1345

Publication Date: 2017/06/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.1342

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Yanbo LU
  Tsinghua University
Jie HAO
  Tsinghua University
Shu-Tao XIA
  Tsinghua University

Keyword

linear codes, erasure codes, code locality, locally repairable codes, distance bounds

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Yanbo LU, Jie HAO, Shu-Tao XIA, "On the Single-Parity Locally Repairable Codes" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 6, pp. 1342-1345, June 2017, doi: 10.1587/transfun.E100.A.1342.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.1342/_p

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@ARTICLE{e100-a_6_1342,
author={Yanbo LU, Jie HAO, Shu-Tao XIA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Single-Parity Locally Repairable Codes},
year={2017},
volume={E100-A},
number={6},
pages={1342-1345},
abstract={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.},
keywords={},
doi={10.1587/transfun.E100.A.1342},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - On the Single-Parity Locally Repairable Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1342
EP - 1345
AU - Yanbo LU
AU - Jie HAO
AU - Shu-Tao XIA
PY - 2017
DO - 10.1587/transfun.E100.A.1342
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2017
AB - 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.
ER -