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.
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