  Reconstruction codes are generalizations of error-correcting codes that can
correct errors by a given number of noisy reads. The study of such codes was
initiated by Levenshtein in 2001 and developed recently due to applications in
modern storage devices such as racetrack memories and DNA storage. The central
problem on this topic is to design codes with redundancy as small as possible
for a given number $N$ of noisy reads. In this paper, the minimum redundancy of
such codes for binary channels with exactly two insertions is determined
asymptotically for all values of $N\ge 5$. Previously, such codes were studied
only for channels with single edit errors or two-deletion errors.
