On the Optimality of Gabidulin-Based LRCs as Codes with Multiple Local Erasure Correction

Geonu KIM; Jungwoo LEE

doi:10.1587/transfun.E102.A.1326

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On the Optimality of Gabidulin-Based LRCs as Codes with Multiple Local Erasure Correction

Geonu KIM, Jungwoo LEE

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Summary :

The Gabidulin-based locally repairable code (LRC) construction by Silberstein et al. is an important example of distance optimal (r,δ)-LRCs. Its distance optimality has been further shown to cover the case of multiple (r,δ)-locality, where the (r,δ)-locality constraints are different among different symbols. However, the optimality only holds under the ordered (r,δ) condition, where the parameters of the multiple (r,δ)-locality satisfy a specific ordering condition. In this letter, we show that Gabidulin-based LRCs are still distance optimal even without the ordered (r,δ) condition.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.9 pp.1326-1329

Publication Date: 2019/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E102.A.1326

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Geonu KIM
Seoul National University
Jungwoo LEE
Seoul National University

Keyword

locally repairable codes, multiple locality, local erasure correction, Gabidulin code

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Geonu KIM, Jungwoo LEE, "On the Optimality of Gabidulin-Based LRCs as Codes with Multiple Local Erasure Correction" in IEICE TRANSACTIONS on Fundamentals, vol. E102-A, no. 9, pp. 1326-1329, September 2019, doi: 10.1587/transfun.E102.A.1326.
Abstract: The Gabidulin-based locally repairable code (LRC) construction by Silberstein et al. is an important example of distance optimal (r,δ)-LRCs. Its distance optimality has been further shown to cover the case of multiple (r,δ)-locality, where the (r,δ)-locality constraints are different among different symbols. However, the optimality only holds under the ordered (r,δ) condition, where the parameters of the multiple (r,δ)-locality satisfy a specific ordering condition. In this letter, we show that Gabidulin-based LRCs are still distance optimal even without the ordered (r,δ) condition.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1326/_p

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@ARTICLE{e102-a_9_1326,
author={Geonu KIM, Jungwoo LEE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Optimality of Gabidulin-Based LRCs as Codes with Multiple Local Erasure Correction},
year={2019},
volume={E102-A},
number={9},
pages={1326-1329},
abstract={The Gabidulin-based locally repairable code (LRC) construction by Silberstein et al. is an important example of distance optimal (r,δ)-LRCs. Its distance optimality has been further shown to cover the case of multiple (r,δ)-locality, where the (r,δ)-locality constraints are different among different symbols. However, the optimality only holds under the ordered (r,δ) condition, where the parameters of the multiple (r,δ)-locality satisfy a specific ordering condition. In this letter, we show that Gabidulin-based LRCs are still distance optimal even without the ordered (r,δ) condition.},
keywords={},
doi={10.1587/transfun.E102.A.1326},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - On the Optimality of Gabidulin-Based LRCs as Codes with Multiple Local Erasure Correction
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1326
EP - 1329
AU - Geonu KIM
AU - Jungwoo LEE
PY - 2019
DO - 10.1587/transfun.E102.A.1326
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2019
AB - The Gabidulin-based locally repairable code (LRC) construction by Silberstein et al. is an important example of distance optimal (r,δ)-LRCs. Its distance optimality has been further shown to cover the case of multiple (r,δ)-locality, where the (r,δ)-locality constraints are different among different symbols. However, the optimality only holds under the ordered (r,δ) condition, where the parameters of the multiple (r,δ)-locality satisfy a specific ordering condition. In this letter, we show that Gabidulin-based LRCs are still distance optimal even without the ordered (r,δ) condition.
ER -