  An identifying code in a graph is a subset of vertices having a nonempty and
distinct intersection with the closed neighborhood of every vertex. We prove
that the infimum density of any identifying code in $S_k$ (an infinite strip of
$k$ rows in the square grid) can always be achieved by a periodic identifying
code with pattern length at most $2^{4k}$. Assisted by a compute program
implementing Karp's algorithm for minimum cycle mean, we find a periodic
identifying code in $S_4$ with the minimum density $11/28$, and a periodic
identifying code in $S_5$ with the minimum density $19/50$.
