Weight of duals of BCH codes and exponential sums

AbstractWe consider a binary BCH code Cm of length 2m–1. If m is odd, we improve the bound on the distance of the dual of Cm previously given by Carlitz–Uchiyama, Serre and Moreno–Moreno

Nonlinarity of Boolean functions and hyperelliptic curves

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

Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents

International audienceWe prove a necessary condition for some polynomials of Gold and Kasami degree to be APN over F q n for large n

On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2

International audienceLet t be an integer ≥ 3 such that t ≡ 1 mod 4. The absolute irreducibility of the polynomial ϕt(x,y)=xt+yt+1+(x+y+1)t(x+y)(x+1)(y+1) (over F2) plays an important role in the study of APN functions. We prove that this polynomial is absolutely irreducible under the assumptions that the largest odd integer which divides t − 1 is large enough and can not be written in a specific form

Non linéarité des fonctions booléennes données par des traces de polynômes de degré binaire 3

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 of binary degree equal to 3. 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

Besoins de recherches (en écotoxicologie) en lien avec les politiques publiques

[Departement_IRSTEA]Eaux [TR1_IRSTEA]BELCAInternational audiencePublic policies that intend to protect ecosystems or human health from toxic impairments in the environment need to be as much evidence based as possible. The precautionary principle applies when little or no evidence is available. This is the case for unknown risks from new or non assessed chemicals in the environment. Moving from precaution to prevention where enough evidence is available for sound decisions implies developing research actions or research strategies