Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes

Abhishek Agarwal, Alexander Barg, Sihuang Hu, Arya Mazumdar, Itzhak Tamo

Research output: Contribution to journalArticlepeer-review


Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered by accessing only a small number of other symbols. For LRC codes over a small alphabet (such as binary), the optimal rate-distance trade-off is unknown. We present several new combinatorial bounds on LRC codes including the locality-aware sphere packing and Plotkin bounds. We also develop an approach to linear programming (LP) bounds on LRC codes. The resulting LP bound gives better estimates in examples than the other upper bounds known in the literature. Further, we provide the tightest known upper bound on the rate of linear LRC codes with a given relative distance, an improvement over the previous best known bounds.

Original languageEnglish
Pages (from-to)3481-3492
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - May 2018


  • LRPC codes
  • Recursive upper bounds
  • coset graphs
  • linear programming bounds
  • product association schemes


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