The authors give explicit (n, N; B)-reconstruction codes for constant N in {5,9,11,14} with redundancies 3 log n + 4, 2 log n + 12 log log n + O(1), log n + 12 log log n + O(1), and log n + 3 respectively.
Sequence reconstruction over the deletion channel,
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Correcting One Deletion and One Substitution with a Constant Number of Reads
The authors give explicit (n, N; B)-reconstruction codes for constant N in {5,9,11,14} with redundancies 3 log n + 4, 2 log n + 12 log log n + O(1), log n + 12 log log n + O(1), and log n + 3 respectively.