arXiv subjects
Publications and source records attributed to Eric Férard.
Nous étudions la non linéarité des fonctions définies sur F_{2^m} où $m$ est un entier impair, associées aux polynômes de degré 7 ou à des polynômes plus généraux. ----- We study the nonlinearity of the functions defined on F_{2^m} where $m$ is an odd integer, associated to the polynomials of degree 7 or more general polynomials.
We study the nonlinearity of functions defined on a finite field with 2^m elements which are the trace of a polynomial of degree 7 or more general polynomials. We show that for m odd such functions have rather good nonlinearity properties. We use for that recent results of Maisner and Nart about zeta functions of supersingular curves of genus 2. We give some criterion for a vectorial function not to be almost perfect nonlinear.
In this paper we consider the Newton polygons of $L$-functions coming from additive exponential sums associated to a polynomial over a finite field $\F_q$. These polygons define a stratification of the space of polynomials of fixed degree. We determine the open stratum: we give the generic Newton polygon for polynomials of degree $d\geq 2$ when the characteristic $p$ is greater than 3d, and the Hasse polynomial, i.e. the equation defining the hypersurface complementary to the open stratum.