  We consider the problem of constructing binary codes for correcting deletions
that are localized within certain parts of the codeword that are unknown a
priori. The model that we study is when $\delta \leq w$ deletions are localized
in a window of size $w$ bits. These $\delta$ deletions do not necessarily occur
in consecutive positions, but are restricted to the window of size $w$. The
localized deletions model is a generalization of the bursty model, in which all
the deleted bits are consecutive. In this paper, we construct new explicit
codes for the localized model, based on the family of Guess & Check codes which
was previously introduced by the authors. The codes that we construct can
correct, with high probability, $\delta \leq w$ deletions that are localized in
a single window of size $w$, where $w$ grows with the block length. Moreover,
these codes are systematic; have low redundancy; and have efficient
deterministic encoding and decoding algorithms. We also generalize these codes
to deletions that are localized within multiple windows in the codeword.
