Context : 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 \lesssim 5 star-forming galaxies , where we can still directly observe their ionizing radiation .

Aims : The aim of this work is to explore the correlation between the LyC emission and some of the proposed indirect indicators of LyC radiation at z \sim 4 such as a bright Ly \alpha emission and a compact UV continuum size .

Methods : We selected a sample of 201 star-forming galaxies from the Vimos Ultra Deep Survey ( VUDS ) at 3.5 \leq z \leq 4.3 in the COSMOS , ECDFS and VVDS-2h fields , including only those with reliable spectroscopic redshifts , a clean spectrum in the LyC range and clearly not contaminated by bright nearby sources in the same slit .
For all galaxies we have measured the Ly \alpha EW , the Ly \alpha velocity shift with respect to the systemic redshift , the Ly \alpha spatial extension and the UV continuum effective radius .
We then selected different sub-samples according to the properties predicted to be good LyC emission indicators : in particular we created sub-samples of galaxies with EW ( Ly \alpha ) \geq 70 \AA , Ly \alpha _ { ext } \leq 5.7 kpc , r _ { UV } \leq 0.30 kpc and | \Delta v _ { Ly \alpha } | \leq 200 km / s .
We stacked all the galaxies in each sub-sample and measured the flux density ratio ( f _ { \lambda } ( 895 ) / f _ { \lambda } ( 1470 ) ) , that we consider to be a proxy for LyC emission , and compared these ratios to those obtained for the complementary samples .
Finally , to estimate the statistical contamination from lower redshift interlopers in our samples , we performed dedicated Monte Carlo simulations using an ultradeep U-band image of the ECDFS field .

Results : We find that the stacks of galaxies which are UV compact ( r _ { UV } \leq 0.30 kpc ) and have bright Ly \alpha emission ( EW ( Ly \alpha ) \geq 70 \AA ) , have much higher LyC fluxes compared to the rest of the galaxy population .
These parameters appear to be good indicators of LyC radiation in agreement with theoretical studies and previous observational works .
In addition we find that galaxies with a low Ly \alpha spatial extent ( Ly \alpha _ { ext } \leq 5.7 kpc ) have higher LyC flux compared to the rest of the population : such a correlation had never been analysed before and seems even stronger than the correlation with high EW ( Ly \alpha ) and small r _ { UV } .
These results assume that the stacks from all the sub-samples present the same statistical contamination from lower redshift interlopers .
If we subtract a statistical contamination from low redshift interlopers obtained with the simulations from the flux density ratios ( f _ { \lambda } ( 895 ) / f _ { \lambda } ( 1470 ) ) of the significant sub-samples we find that these samples contain real LyC leaking flux with a very high probability , although the true average escape fractions are very uncertain .

Conclusions : Our work indicates that galaxies with very high EW ( Ly \alpha ) , small Ly \alpha _ { ext } and small r _ { UV } are very likely the best candidates to show Lyman Continuum radiation at z \sim 4 and could therefore be the galaxies that contributed more to reionization .