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We present 15-GHz Karl G. Jansky Very Large Array observations of a completesample of radio galaxies selected at 15.7 GHz from the Tenth Cambridge (10C)survey. 67 out of the 95 sources (71 per cent) are unresolved in the newobservations and lower-frequency radio observations, placing an upper limit ontheir angular size of ~2 arcsec. Thus compact radio galaxies, or radio galaxieswith very faint jets, are the dominant population in the 10C survey. Thisprovides support for the suggestion in our previous work that low-luminosity($L<10^{25} \, \textrm{W Hz}^{-1}$) radio galaxies are core-dominated, althoughhigher-resolution observations are required to confirm this directly. The 10Csample of compact, high-frequency selected radio galaxies is a mixture ofhigh-excitation and low-excitation radio galaxies and displays a range of radiospectral shapes, demonstrating that they are a mixed population of objects.

The faint radio source population at 15.7 GHz -- IV. The dominance of core emission in faint radio galaxies