IEICE TRANSACTIONS on Fundamentals
Singleton-Type Optimal LRCs with Minimum Distance 3 and 4 from Projective Code
Summary :
Locally repairable codes (LRCs) are implemented in distributed storage systems (DSSs) due to their low repair overhead. The locality of an LRC is the number of nodes in DSSs that participate in the repair of failed nodes, which characterizes the repair cost. An LRC is called optimal if its minimum distance attains the Singleton-type upper bound [1]. In this letter, optimal LRCs are considered. Using the concept of projective code in projective space PG(k, q) and shortening strategy, LRCs with d=3 are proposed. Meantime, derived from an ovoid [q2+1, 4, q2]q code (responding to a maximal (q2+1)-cap in PG(3, q)), optimal LRCs over Fq with d=4 are constructed.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.1 pp.319-323
- Publication Date
- 2021/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2019EAL2158
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Qiang FU
Air Force Engineering University
Ruihu LI
Air Force Engineering University
Luobin GUO
Air Force Engineering University
Gang CHEN
Keyword
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Qiang FU, Ruihu LI, Luobin GUO, Gang CHEN, "Singleton-Type Optimal LRCs with Minimum Distance 3 and 4 from Projective Code" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 1, pp. 319-323, January 2021, doi: 10.1587/transfun.2019EAL2158.
Abstract: Locally repairable codes (LRCs) are implemented in distributed storage systems (DSSs) due to their low repair overhead. The locality of an LRC is the number of nodes in DSSs that participate in the repair of failed nodes, which characterizes the repair cost. An LRC is called optimal if its minimum distance attains the Singleton-type upper bound [1]. In this letter, optimal LRCs are considered. Using the concept of projective code in projective space PG(k, q) and shortening strategy, LRCs with d=3 are proposed. Meantime, derived from an ovoid [q2+1, 4, q2]q code (responding to a maximal (q2+1)-cap in PG(3, q)), optimal LRCs over Fq with d=4 are constructed.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAL2158/_p
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@ARTICLE{e104-a_1_319,
author={Qiang FU, Ruihu LI, Luobin GUO, Gang CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Singleton-Type Optimal LRCs with Minimum Distance 3 and 4 from Projective Code},
year={2021},
volume={E104-A},
number={1},
pages={319-323},
abstract={Locally repairable codes (LRCs) are implemented in distributed storage systems (DSSs) due to their low repair overhead. The locality of an LRC is the number of nodes in DSSs that participate in the repair of failed nodes, which characterizes the repair cost. An LRC is called optimal if its minimum distance attains the Singleton-type upper bound [1]. In this letter, optimal LRCs are considered. Using the concept of projective code in projective space PG(k, q) and shortening strategy, LRCs with d=3 are proposed. Meantime, derived from an ovoid [q2+1, 4, q2]q code (responding to a maximal (q2+1)-cap in PG(3, q)), optimal LRCs over Fq with d=4 are constructed.},
keywords={},
doi={10.1587/transfun.2019EAL2158},
ISSN={1745-1337},
month={January},}
Copy
TY - JOUR
TI - Singleton-Type Optimal LRCs with Minimum Distance 3 and 4 from Projective Code
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 319
EP - 323
AU - Qiang FU
AU - Ruihu LI
AU - Luobin GUO
AU - Gang CHEN
PY - 2021
DO - 10.1587/transfun.2019EAL2158
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2021
AB - Locally repairable codes (LRCs) are implemented in distributed storage systems (DSSs) due to their low repair overhead. The locality of an LRC is the number of nodes in DSSs that participate in the repair of failed nodes, which characterizes the repair cost. An LRC is called optimal if its minimum distance attains the Singleton-type upper bound [1]. In this letter, optimal LRCs are considered. Using the concept of projective code in projective space PG(k, q) and shortening strategy, LRCs with d=3 are proposed. Meantime, derived from an ovoid [q2+1, 4, q2]q code (responding to a maximal (q2+1)-cap in PG(3, q)), optimal LRCs over Fq with d=4 are constructed.
ER -
English
