A sample of 6C radio sources designed to find objects at redshift z>4 -: I.: The radio data

We describe the selection of a sample of 34 radio sources from the 6C survey from a region of sky covering 0.133 sr, The selection criteria for this sample, hereafter called 6C*, were chosen to optimize the chances of finding radio galaxies at redshift z > 4. Optical follow-up observations have already led to the discovery of the most distant known radio galaxy at z = 4.41. We present VLA radio maps and derive radio spectra for all the 6C* objects.