  A sample of 2712 radio-luminous galaxies is defined from the second data
release of the Sloan Digital Sky Survey (SDSS) by cross-comparing the main
spectroscopic galaxy sample with two radio surveys: the NRAO VLA Sky Survey
(NVSS) and the Faint Images of the Radio Sky at Twenty centimetres (FIRST)
survey. The comparison is carried out in a multi-stage process and makes
optimal use of both radio surveys by exploiting the sensitivity of the NVSS to
extended and multi-component radio sources in addition to the high angular
resolution of the FIRST images. A radio source sample with 95% completeness and
98.9% reliability is achieved, far better than would be possible for this
sample if only one of the surveys was used. The radio source sample is then
divided into two classes: radio-loud AGN and galaxies in which the radio
emission is dominated by star formation. The division is based on the location
of a galaxy in the plane of 4000Ang break strength versus radio luminosity per
unit stellar mass and provides a sample of 2215 radio-loud AGN and 497 star
forming galaxies brighter than 5mJy at 1.4GHz. A full catalogue of positions
and radio properties is provided for these sources. The local radio luminosity
function is then derived both for radio-loud AGN and for star-forming galaxies
and is found to be in agreement with previous studies. By using the radio to
far-IR correlation, the radio luminosity function of star forming galaxies is
also compared to the luminosity function derived in the far-infrared. It is
found to agree well at high luminosities but less so at lower luminosities,
confirming that the linearity of the radio to far-IR correlation breaks down
below about 10^22 W/Hz at 1.4GHz.
