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.