Optimal Locally Repairable Codes: An Improved Bound and Constructions

Han Cai; Cuiling Fan; Ying Miao; Moshe Schwartz; Xiaohu Tang

doi:10.1109/TIT.2022.3161613

Optimal Locally Repairable Codes: An Improved Bound and Constructions

Han Cai, Cuiling Fan, Ying Miao, Moshe Schwartz, Xiaohu Tang

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

Original language	English
Pages (from-to)	5060-5074
Number of pages	15
Journal	IEEE Transactions on Information Theory
Issue number	8
DOIs	https://doi.org/10.1109/TIT.2022.3161613
State	Accepted/In press - 1 Jan 2022

Keywords

Codes
Fans
Generators
Hamming distance
Linear codes
Locally repairable codes
Maintenance engineering
Singleton-type bound
Upper bound

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2022.3161613

Cite this

@article{168c2189039d4422b79692eae193c096,

title = "Optimal Locally Repairable Codes: An Improved Bound and Constructions",

abstract = "We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.",

keywords = "Codes, Fans, Generators, Hamming distance, Linear codes, Locally repairable codes, Maintenance engineering, Singleton-type bound, Upper bound",

author = "Han Cai and Cuiling Fan and Ying Miao and Moshe Schwartz and Xiaohu Tang",

note = "Publisher Copyright: IEEE",

year = "2022",

month = jan,

day = "1",

doi = "10.1109/TIT.2022.3161613",

language = "English",

pages = "5060--5074",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "8",

}

TY - JOUR

T1 - Optimal Locally Repairable Codes

T2 - An Improved Bound and Constructions

AU - Cai, Han

AU - Fan, Cuiling

AU - Miao, Ying

AU - Schwartz, Moshe

AU - Tang, Xiaohu

N1 - Publisher Copyright: IEEE

PY - 2022/1/1

Y1 - 2022/1/1

N2 - We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

AB - We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

KW - Codes

KW - Fans

KW - Generators

KW - Hamming distance

KW - Linear codes

KW - Locally repairable codes

KW - Maintenance engineering

KW - Singleton-type bound

KW - Upper bound

UR - http://www.scopus.com/inward/record.url?scp=85127078608&partnerID=8YFLogxK

U2 - 10.1109/TIT.2022.3161613

DO - 10.1109/TIT.2022.3161613

M3 - Article

SN - 0018-9448

SP - 5060

EP - 5074

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 8

ER -

Optimal Locally Repairable Codes: An Improved Bound and Constructions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this