Optimal Locally Repairable Codes: An Improved Bound and Constructions

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish
Pages (from-to)5060-5074
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number8
StateAccepted/In press - 1 Jan 2022


  • 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


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