  We report on multi-frequency linear polarization monitoring of 15 active
galactic nuclei containing highly relativistic jets with apparent speeds from
$\sim$4 $c$ to $>40c$. The measurements were obtained at optical, 1 mm, and 3
mm wavelengths, and at 7 mm with the Very Long Baseline Array. The data show a
wide range in degree of linear polarization among the sources, from $<$1% to
$>$30%, and interday polarization variability in individual sources. The
polarization properties suggest separation of the sample into three groups with
low, intermediate, and high variability of polarization in the core at 7 mm :
LVP, IVP, and HVP, respectively. The groups are partially associated with the
common classification of active galactic nuclei as radio galaxies and quasars
with low optical polarization (LVP), BL Lacertae objects (IVP), and highly
optically polarized quasars (HVP). Our study investigates correlations between
total flux, fractional polarization, and polarization position angle at the
different wavelengths. We interpret the polarization properties of the sources
in the sample through models in which weak shocks compress turbulent plasma in
the jet. The differences in the orientation of sources with respect to the
observer, jet kinematics, and abundance of thermal matter external to the jet
near the core can account for the diversity in the polarization properties. The
results provide strong evidence that the optical polarized emission originates
in shocks, most likely situated between the 3 mm and 7 mm VLBI cores. They also
support the idea that the 1 mm core lies at the edge of the transition zone
between electromagnetically dominated and turbulent hydrodynamical sections of
the jet.
