The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Les systèmes de stockage distribués modernes à grande échelle jouent un rôle central dans les centres de données et le stockage cloud, tandis que les pannes de nœuds dans les centres de données sont courantes. Les données perdues dans le nœud défaillant doivent être récupérées efficacement. Les codes réparables localement (LRC) sont conçus pour résoudre ce problème. La localité d'un LRC est le nombre de nœuds qui participent à la récupération des données perdues suite à une défaillance du nœud, ce qui caractérise l'efficacité de la réparation. Un LRC est dit optimal si sa distance minimale atteint la limite supérieure de type Singleton [1]. Dans cet article, en utilisant des techniques de base de l'algèbre linéaire sur un champ fini, des LRC optimaux infinis sur des champs d'extension sont dérivés d'un LRC optimal donné sur un champ de base (ou un petit champ). Ensuite, cet article étudie la relation entre les codes proches du MDS avec certaines contraintes et les LRC, et propose en outre un algorithme pour déterminer la localité du dual d'un code linéaire donné. Enfin, sur la base des codes proches du MDS et de l'algorithme proposé, les LRC optimaux obtenus sont présentés.
Qiang FU
Air Force Engineering University
Buhong WANG
Air Force Engineering University
Ruihu LI
Air Force Engineering University
Ruipan YANG
Air Force Engineering University
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Qiang FU, Buhong WANG, Ruihu LI, Ruipan YANG, "Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 8, pp. 1051-1056, August 2023, doi: 10.1587/transfun.2022EAP1107.
Abstract: Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAP1107/_p
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@ARTICLE{e106-a_8_1051,
author={Qiang FU, Buhong WANG, Ruihu LI, Ruipan YANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes},
year={2023},
volume={E106-A},
number={8},
pages={1051-1056},
abstract={Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.},
keywords={},
doi={10.1587/transfun.2022EAP1107},
ISSN={1745-1337},
month={August},}
Copier
TY - JOUR
TI - Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1051
EP - 1056
AU - Qiang FU
AU - Buhong WANG
AU - Ruihu LI
AU - Ruipan YANG
PY - 2023
DO - 10.1587/transfun.2022EAP1107
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2023
AB - Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.
ER -