Abstract
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 language | English |
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Pages (from-to) | 157-195 |
Number of pages | 39 |
Journal | SIAM Journal on Computing |
Volume | 49 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jan 2020 |
Externally published | Yes |
Keywords
- List decoding
- List recvoery
- Local decoding
ASJC Scopus subject areas
- General Computer Science
- General Mathematics