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

Non-linearity of the Carlet-Feng function, and repartition of Gauss sums