On Optimal Locally Repairable Codes and Generalized Sector-Disk Codes

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Abstract

Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this article. The length of the constructed codes is super-linear in the alphabet size, which improves upon the well known pyramid codes, whose length is only linear in the alphabet size. The recoverable erasure patterns are also analyzed for the new codes. Based on the recoverable erasure patterns, we construct generalized sector-disk (GSD) codes, which can recover from disk erasures mixed with sector erasures in a more general setting than known sector-disk (SD) codes. Additionally, the number of sectors in the constructed GSD codes is super-linear in the alphabet size, compared with known SD codes, whose number of sectors is only linear in the alphabet size.

Original languageEnglish
Article number9256276
Pages (from-to)686-704
Number of pages19
JournalIEEE Transactions on Information Theory
Volume67
Issue number2
DOIs
StatePublished - 1 Feb 2021

Keywords

  • Distributed storage
  • Goppa codes
  • locally repairable codes
  • sector-disk codes

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