A Construction of Maximally Recoverable Codes with Order-Optimal Field Size

Han Cai; Ying Miao; Moshe Schwartz; Xiaohu Tang

doi:https://doi.org/10.1109/TIT.2021.3120016

A Construction of Maximally Recoverable Codes with Order-Optimal Field Size

Han Cai, Ying Miao, Moshe Schwartz, Xiaohu Tang

Department of Electrical & Computer Engineering

Ben-Gurion University of the Negev

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

Abstract

We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.

Original language	American English
Pages (from-to)	204-212
Number of pages	9
Journal	IEEE Transactions on Information Theory
Volume	68
Issue number	1
DOIs	https://doi.org/10.1109/TIT.2021.3120016
State	Published - 1 Jan 2022

Keywords

Distributed storage
linearized Reed-Solomon codes
locally repairable codes
maximally recoverable codes
partial MDS codes
sum-rank metric

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

https://doi.org/10.1109/TIT.2021.3120016

Cite this

@article{bfadff4eba274a2c9d3837c035e1fafd,

title = "A Construction of Maximally Recoverable Codes with Order-Optimal Field Size",

abstract = "We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.",

keywords = "Distributed storage, linearized Reed-Solomon codes, locally repairable codes, maximally recoverable codes, partial MDS codes, sum-rank metric",

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

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2022",

month = jan,

day = "1",

doi = "https://doi.org/10.1109/TIT.2021.3120016",

language = "American English",

volume = "68",

pages = "204--212",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

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

number = "1",

}

TY - JOUR

T1 - A Construction of Maximally Recoverable Codes with Order-Optimal Field Size

AU - Cai, Han

AU - Miao, Ying

AU - Schwartz, Moshe

AU - Tang, Xiaohu

PY - 2022/1/1

Y1 - 2022/1/1

N2 - We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.

AB - We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.

KW - Distributed storage

KW - linearized Reed-Solomon codes

KW - locally repairable codes

KW - maximally recoverable codes

KW - partial MDS codes

KW - sum-rank metric

UR - http://www.scopus.com/inward/record.url?scp=85117753845&partnerID=8YFLogxK

U2 - https://doi.org/10.1109/TIT.2021.3120016

DO - https://doi.org/10.1109/TIT.2021.3120016

M3 - Article

SN - 0018-9448

VL - 68

SP - 204

EP - 212

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 1

ER -

A Construction of Maximally Recoverable Codes with Order-Optimal Field Size

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this