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

Han Cai; Ying Miao; Moshe Schwartz; Xiaohu Tang

doi: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

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

25 Scopus citations

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	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

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2021.3120016

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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",

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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.

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KW - linearized Reed-Solomon codes

KW - locally repairable codes

KW - maximally recoverable codes

KW - partial MDS codes

KW - sum-rank metric

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

Abstract

Keywords

ASJC Scopus subject areas

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