On the List Recoverability of Randomly Punctured Codes

Authors Ben Lund , Aditya Potukuchi

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Author Details

Ben Lund
  • Department of Mathematics, Princeton University, NJ, USA
Aditya Potukuchi
  • Department of Computer Science, Rutgers University, Piscataway, NJ, USA


We thank Venkat Guruswami, Jeff Kahn, Swastik Kopparty, Noga Ron-Zewi, and Mary Wootters for helpful discussions. We also thank an anonymous reviewer for helpful comments on the presentation of the results.

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Ben Lund and Aditya Potukuchi. On the List Recoverability of Randomly Punctured Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 30:1-30:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Error-correcting codes
  • List recovery
  • randomly punctured codes
  • Reed-Solomon codes


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