**Checking Helleseth's conjecture in dimension less or equal to 32**

This page reports the numerical experiments (January 2012)
related to numerical verification of Helleseth's conjecture in
dimension less or equal to 32.

### Helleseth'conjecture

Let m be a positive integer, X a nontrivial additive character
of GF(2,m). The Helleseth's conjecture claims that for all
integer s coprime with (2^m-1), there exists a non zero element
a in GF(2,m) such that

sum_{x in GF(2,m)} X( x^s + ax ) = 0.
execpt in the case where s = 1, 2, 4 etc...
### Numerical facts

Helleseth conjecture is true for all m less than 26, and it
is true for all even m less or equal to 32. Note that the
first point was done
here. In this page, we explain how to get the second point.

### Methodology

Philippe Langevin, Last modification January 2012.