  To identify the galaxies responsible for the reionization of the Universe, we
must rely on the investigation of the Lyman Continuum (LyC) properties of z<5
star-forming galaxies, where we can still directly observe their ionizing
radiation. We selected a sample of 201 star-forming galaxies from the Vimos
Ultra Deep Survey at 3.5<z<4.3 to explore the validity of some of the proposed
indirect indicators of LyC radiation. We created subsamples of galaxies with
EWLya>70{\AA}, Lya(ext)<5.7kpc, rUV<0.3kpc and |Dv Lya|<200km/s, stacked all
the galaxies in each subsample and measured the flux density ratio
fnu(895)/fnu(1470), that we consider to be a proxy for LyC emission. We
compared these ratios to those obtained for the complementary samples. We find
that the stacks of galaxies which are UV compact (rUV<0.3kpc) and have bright
Lya emission (EWLya>70{\AA}), have much higher LyC fluxes compared to the rest
of the galaxy population in agreement with theoretical studies and previous
observational works. We also find that galaxies with low Lya(ext) have the
highest LyC flux: this new correlation seems even stronger than the
correlations with high EWLya and small rUV. These results assume that the
stacks from all the subsamples present the same statistical contamination from
lower redshift interlopers. If we subtract a statistical contamination from low
redshift interlopers obtained with dedicated Monte Carlo simulations, from the
flux density ratios (fnu(895)/fnu(1470)) of the significant subsamples we find
that these samples contain real LyC leaking flux with a very high probability,
but the true average escape fractions remain uncertain. Our work indicates that
galaxies with very high EWLya, small Lya(ext) and small rUV are very likely the
best candidates to show LyC radiation at z=4 and could therefore be the
galaxies that contributed more to reionization.
