The SUrvey for Pulsars and Extragalactic Radio Bursts - III. Polarization properties of FRBs 160102 and 151230

We report on the polarization properties of two fast radio bursts (FRBs): 151230 and 160102 discovered in the SUrvey for Pulsars and Extragalactic Radio Bursts (SUPERB) at the Parkes Radio Telescope. FRB 151230 is observed to be 6 +/- 11 per cent circularly polarized and 35 +/- 13 per cent linearly polarized with a rotation measure (RM) consistent with zero. Conversely, FRB 160102 is observed to have a circular polarization fraction of 30 +/- 11 per cent, linear polarization fraction of 84 +/- 15 per cent for RM = -221(6) radm(-2), and the highest measured dispersion measure (2596.1 +/- 0.3 pc cm(-3)) for an FRB to date. We examine possible progenitor models for FRB 160102 in extragalactic, non-cosmological and cosmological scenarios. After accounting for the Galactic foreground contribution, we estimate the intrinsic RM to be -256(9) rad m(-2) in the low-redshift case and similar to-2.4x10(2) rad m(-2) in the high-redshift case. We assess the relative likeliness of these scenarios and how each can be tested. We also place constraints on the scattering measure and study the impact of scattering on the signal's polarization position angle.