For every small eta, explicit binary linear list-decodable codes correct an eta fraction of insertions and deletions with rate 1-O(eta^(1/4)) and polynomial-time encoding and decoding.
Local list recovery of high-rate tensor codes and applications,
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Linear List Decodable Edit-Correcting Codes with Rate Approaching $1$
For every small eta, explicit binary linear list-decodable codes correct an eta fraction of insertions and deletions with rate 1-O(eta^(1/4)) and polynomial-time encoding and decoding.