  We present a high angular resolution ($\sim 0.2^{\prime\prime}$), high
sensitivity ($\sigma \sim 0.2$ mJy) survey of the 870 $\mu$m continuum emission
from the circumstellar material around 49 pre-main sequence stars in the $\rho$
Ophiuchus molecular cloud. Because most millimeter instruments have resided in
the northern hemisphere, this represents the largest high-resolution,
millimeter-wave survey of the circumstellar disk content of this cloud. Our
survey of 49 systems comprises 63 stars; we detect disks associated with 29
single sources, 11 binaries, 3 triple systems and 4 transition disks. We
present flux and radius distributions for these systems; in particular, this is
the first presentation of a reasonably complete probability distribution of
disk radii at millimeter-wavelengths. We also compare the flux distribution of
these protoplanetary disks with that of the disk population of the
Taurus-Auriga molecular cloud. We find that disks in binaries are both
significantly smaller and have much less flux than their counterparts around
isolated stars. We compute truncation calculations on our binary sources and
find that these disks are too small to have been affected by tidal truncation
and posit some explanations for this. Lastly, our survey found 3 candidate
gapped disks, one of which is a newly identified transition disk with no
signature of a dip in infrared excess in extant observations.
