On Optimal Locally Repairable Codes with Super-Linear Length

Han Cai; Ying Miao; Moshe Schwartz; Xiaohu Tang

doi:10.1109/TIT.2020.2977647

On Optimal Locally Repairable Codes with Super-Linear Length

Han Cai, Ying Miao, Moshe Schwartz, Xiaohu Tang

Department of Electrical & Computer Engineering

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

52 Scopus citations

Abstract

In this paper, locally repairable codes which have optimal minimum Hamming distance with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds apply to more general cases, and have weaker requirements compared with the known ones. In this sense, they both improve and generalize previously known bounds. Further, optimal codes are constructed, whose length is order-optimal with respect to the new upper bounds. Notably, the length of the codes is super-linear in the alphabet size.

Original language	English
Article number	9020142
Pages (from-to)	4853-4868
Number of pages	16
Journal	IEEE Transactions on Information Theory
Volume	66
Issue number	8
DOIs	https://doi.org/10.1109/TIT.2020.2977647
State	Published - 1 Aug 2020

Keywords

Distributed storage
Steiner systems
locally repairable codes
packings

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2020.2977647

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abstract = "In this paper, locally repairable codes which have optimal minimum Hamming distance with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds apply to more general cases, and have weaker requirements compared with the known ones. In this sense, they both improve and generalize previously known bounds. Further, optimal codes are constructed, whose length is order-optimal with respect to the new upper bounds. Notably, the length of the codes is super-linear in the alphabet size.",

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AB - In this paper, locally repairable codes which have optimal minimum Hamming distance with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds apply to more general cases, and have weaker requirements compared with the known ones. In this sense, they both improve and generalize previously known bounds. Further, optimal codes are constructed, whose length is order-optimal with respect to the new upper bounds. Notably, the length of the codes is super-linear in the alphabet size.

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On Optimal Locally Repairable Codes with Super-Linear Length

Abstract

Keywords

ASJC Scopus subject areas

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