  The search for Boolean functions that can withstand the main crypyographic
attacks is essential. In 2008, Carlet and Feng studied a class of functions
which have optimal cryptographic properties with the exception of nonlinearity
for which they give a good but not optimal bound. Carlet and some people who
have also worked on this problem of nonlinearity have asked for a new answer to
this problem. We provide a new solution to improve the evaluation of the
nonlinearity of the Carlet-Feng function, by means of the estimation of the
distribution of Gauss sums. This work is in progress and we give some
suggestions to improve this work.
