Polarized foreground emission is a potential contaminant of attempts to measure the fluctuation power spectrum of highly redshifted 21 cm HI emission from the epoch of reionization. Using the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER), we present limits on the observed power spectra of all four Stokes parameters in two frequency bands, centered at 126 MHz ($z=10.3$) and 164 MHz ($z=7.66$) for a three-month observing campaign of a 32-antenna deployment, for which unpolarized power spectrum results have been reported at $z=7.7$ (Parsons et al 2014) and $7.5 < z < 10.5$ (Jacobs et al 2014). The power spectra in this paper are processed in the same way as in those works, and show no definitive detection of polarized power. This non-detection appears to be largely due to the suppression of polarized power by ionospheric rotation measure fluctuations, which strongly affect Stokes Q and U. We are able to show that the net effect of polarized leakage is a negligible contribution at the levels of of the limits reported in Parsons et al 2014 and Jacobs et al 2014.
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