Local list recovery of high-rate tensor codes and applications

Brett Hemenway, Noga Ron-Zewi, Mary Wootters

Research output: Contribution to journalArticlepeer-review


We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions of high-rate globally list recoverable codes, and using appropriate transformations, we obtain the first capacity-achieving locally list decodable codes (over a large constant size alphabet), and the first capacity-achieving globally list decodable codes with nearly linear time list decoding algorithms. Our techniques are inspired by an approach of Gopalan, Guruswami, and Raghavendra [SIAM J. Comput., 40 (2011), pp. 1432-1462] for list decoding tensor codes.

Original languageEnglish
Pages (from-to)157-195
Number of pages39
JournalSIAM Journal on Computing
Issue number4
StatePublished - 2020

Bibliographical note

Funding Information:
\ast Received by the editors December 18, 2017; accepted for publication (in revised form) May 10, 2019; published electronically October 22, 2019. https://doi.org/10.1137/17M116149X Funding: The first author was supported in part by NSF grant CNS-1513671. The third author was supported in part by NSF grant CCF-1657049. The second and third authors were supported in part by NSF-BSF grants CCF-1814629 and 2017732. \dagger Department of Computer Science, University of Pennsylvania, Philadelphia, PA 19104 (fbrett@ cis.upenn.edu). \ddagger Department of Computer Science, University of Haifa, Haifa 31905, Israel (noga@cs.haifa.ac.il). \S Departments of Computer Science and Electrical Engineering, Stanford University, Stanford, CA 94305 (marykw@stanford.edu).

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.


  • List decoding
  • List recvoery
  • Local decoding

ASJC Scopus subject areas

  • Computer Science (all)
  • Mathematics (all)


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