1. LOCAL LIST RECOVERY OF HIGH-RATE TENSOR CODES AND APPLICATIONS.
- Author
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HEMENWAY, BRETT, RON-ZEWI, NOGA, and WOOTTERS, MARY
- Subjects
- *
DECODING algorithms , *TENSOR products , *LINEAR codes , *BUILDING design & construction , *BLOCK designs - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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