#
Exploration of Near Bent cubics with 9 variables

This page will report the numerical experiments
related to the exploration of near-bent cubics
with 9 variables.

### Status

In preparation.
### Definitions

Let m be a positive odd integer. A Boolean function f from
GF(2)^m into GF(2) is said to be near bent if its Wash
spectrum contains the three values : - 2^(m+1)/2, 0 or +2^(m+1)/2.

### Objectives

The main objective is to explore the Near Bent cubics in dimension 9

### Methodology

We start from the classification of Boolean forms of
degree 3 in 9 variables obtained with Eric Brier in 2003
classification of RM(3,9)*

Let f = h + q a near bent cubic where the
cubic part h and the quadratic part q are
given by their ANF

h = sum_u c_u X^u, q = sum_v b_v X^v
There are 999 classes of cubics. The dimension
of quadratic form is 36, it is a little bit too
large for a naive enumeration.
### Results

Philippe Langevin,
Last modification march 2014.