We obtain a sample of 87 radio-loud QSOs in the redshift range 3.6<z<4.4 by cross-correlating sources in the FIRST radio survey S{1.4GHz} > 1 mJy with star-like objects having r <20.2 in SDSS Data Release 7. Of these 87 QSOs, 80 are spectroscopically classified in previous work (mainly SDSS), and form the training set for a search for additional such sources. We apply our selection to 2,916 FIRST-DR7 pairs and find 15 likely candidates. Seven of these are confirmed as high-redshift quasars, bringing the total to 87. The candidates were selected using a neural-network, which yields 97% completeness (fraction of actual high-z QSOs selected as such) and an efficiency (fraction of candidates which are high-z QSOs) in the range of 47 to 60%. We use this sample to estimate the binned optical luminosity function of radio-loud QSOs at $zsim 4$, and also the LF of the total QSO population and its comoving density. Our results suggest that the radio-loud fraction (RLF) at high z is similar to that at low-z and that other authors may be underestimating the fraction at high-z. Finally, we determine the slope of the optical luminosity function and obtain results consistent with previous studies of radio-loud QSOs and of the whole population of QSOs. The evolution of the luminosity function with redshift was for many years interpreted as a flattening of the bright end slope, but has recently been re-interpreted as strong evolution of the break luminosity for high-z QSOs, and our results, for the radio-loud population, are consistent with this.
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