Polarization of radio emission in extragalactic jets at a sub-milliarcsecond angular resolution holds important clues for understanding the structure of the magnetic field in the inner regions of the jets and in close vicinity of the supermassive black holes in the centers of active galaxies. Space VLBI observations provide a unique tool for polarimetric imaging at a sub-milliarcsecond angular resolution and studying the properties of magnetic field in active galactic nuclei on scales of less than 10^4 gravitational radii. A space VLBI observation of high-redshift quasar TXS 0642+449 (OH 471), made at a wavelength of 18 cm (frequency of 1.6 GHz) as part of the Early Science Programme (ESP) of the RadioAstron} mission, is used here to test the polarimetric performance of the orbiting Space Radio Telescope (SRT) employed by the mission, to establish a methodology for making full Stokes polarimetry with space VLBI at 1.6 GHz, and to study the polarized emission in the target object on sub-milliarcsecond scales. Polarization leakage of the SRT at 18 cm is found to be within 9 percents in amplitude, demonstrating the feasibility of high fidelity polarization imaging with RadioAstron at this wavelength. A polarimetric image of 0642+449 with a resolution of 0.8 mas (signifying an ~4 times improvement over ground VLBI observations at the same wavelength) is obtained. The image shows a compact core-jet structure with low (~2%) polarization and predominantly transverse magnetic field in the nuclear region. The VLBI data also uncover a complex structure of the nuclear region, with two prominent features possibly corresponding to the jet base and a strong recollimation shock. The maximum brightness temperature at the jet base can be as high as 4*10^13 K.
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