Bounds on the Parameters of Locally Recoverable Codes

Itzhak Tamo, Alexander Barg, Alexey Frolov

Research output: Contribution to journalArticlepeer-review


A locally recoverable code (LRC code) is a code over a finite alphabet, such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. In this paper, we derive new finite-length and asymptotic bounds on the parameters of LRC codes. For LRC codes with a single recovering set for every coordinate, we derive an asymptotic Gilbert-Varshamov type bound for LRC codes and find the maximum attainable relative distance of asymptotically good LRC codes. Similar results are established for LRC codes with two disjoint recovering sets for every coordinate. For the case of multiple recovering sets (the availability problem), we derive a lower bound on the parameters using expander graph arguments. Finally, we also derive finite-length upper bounds on the rate and the distance of LRC codes with multiple recovering sets.

Original languageEnglish
Article number7384487
Pages (from-to)3070-3083
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2016


  • Availability problem
  • Gilbert-Varshamov bound
  • asymptotic bounds
  • graph expansion
  • recovery graph


Dive into the research topics of 'Bounds on the Parameters of Locally Recoverable Codes'. Together they form a unique fingerprint.

Cite this