  Binary 0-1 measurement matrices, especially those from coding theory, were
introduced to compressed sensing (CS) recently. Good measurement matrices with
preferred properties, e.g., the restricted isometry property (RIP) and
nullspace property (NSP), have no known general ways to be efficiently checked.
Khajehnejad \emph{et al.} made use of \emph{girth} to certify the good
performances of sparse binary measurement matrices. In this paper, we examine
the performance of binary measurement matrices with uniform column weight and
arbitrary girth under basis pursuit. Explicit sufficient conditions of exact
reconstruction %only including $\gamma$ and $g$ are obtained, which improve the
previous results derived from RIP for any girth $g$ and results from NSP when
$g/2$ is odd. Moreover, we derive explicit $l_1/l_1$, $l_2/l_1$ and
$l_\infty/l_1$ sparse approximation guarantees. These results further show that
large girth has positive impacts on the performance of binary measurement
matrices under basis pursuit, and the binary parity-check matrices of good LDPC
codes are important candidates of measurement matrices.
