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.
|Number of pages||39|
|Journal||SIAM Journal on Computing|
|State||Published - 2020|
Bibliographical noteFunding 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 (email@example.com). \S Departments of Computer Science and Electrical Engineering, Stanford University, Stanford, CA 94305 (firstname.lastname@example.org).
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- List decoding
- List recvoery
- Local decoding
ASJC Scopus subject areas
- Computer Science (all)
- Mathematics (all)