IEICE TRANSACTIONS on Fundamentals
Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial
Summary :
Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.12 pp.2047-2054
- Publication Date
- 2018/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E101.A.2047
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding theory and techniques
Authors
Tomoya HAMADA
University of Electro-Communications
Hideki YAGI
University of Electro-Communications
Keyword
Latest Issue
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Tomoya HAMADA, Hideki YAGI, "Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 12, pp. 2047-2054, December 2018, doi: 10.1587/transfun.E101.A.2047.
Abstract: Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2047/_p
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@ARTICLE{e101-a_12_2047,
author={Tomoya HAMADA, Hideki YAGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial},
year={2018},
volume={E101-A},
number={12},
pages={2047-2054},
abstract={Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.},
keywords={},
doi={10.1587/transfun.E101.A.2047},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2047
EP - 2054
AU - Tomoya HAMADA
AU - Hideki YAGI
PY - 2018
DO - 10.1587/transfun.E101.A.2047
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.
ER -
English
