Kinematics of the Local Universe XIV. Measurements from the 21 cm line and the HI mass function from a homogeneous catalog gathered with the Nanc{c}ay radio telescope

This paper presents 828 new 21 cm neutral hydrogen line measurements carried out with the FORT receiver of the meridian transit Nan\c{c}ay radio telescope (NRT) in the years 2000 -- 2007. This observational program was part of a larger project aimed at collecting an exhaustive and magnitude-complete HI extragalactic catalog for Tully-Fisher applications. Through five massive data releases, the KLUN series has collected a homogeneous sample of 4876 HI-spectra of spiral galaxies, complete down to a flux of 5 Jy.km.s^{-1} and with declination delta > -40{\deg}. We publish here the last release of the KLUN HI observational program, corresponding to the faint end of the survey, with HI masses ranging from 5 10^8 to 5 10^{10} solar masses. The size of this final sample is comparable to the catalogs based on the Arecibo and Parkes radio telescope campaigns, and it allows general HI mass distribution studies from a set of homogeneous radio measurements.