I asked the question to Philippe Langevin by e-mail, here's his answer, hopefully it will help--I am not very au fait with the technicalities of this topic. Here is the link to his projects page referred to below.
I guess you speak about the affine classification of bent functions ?
(1)
In my page projects, I give the FULL classification of quartic forms,
that is the class by means of a representative but also, the most
important (and the meaning of FULL), the stabilizer groups.
I precise this point because without group theory you can not do
miracle! By the way, the full classification of B(6) is also on my
website project.
After that, you can effectively enumerate the classes of bent
functions, the job is done in our article with Pascal,
Jean-Pierre, and Gregor.
writing a bent function as :
$H + C + Q$
where H is homogeneous of degree 4, C of degree C and Q of degree 2,
We start from 536 quartic forms H, then we have to discover the
full classification of the H+C, and finaly the H+C+Q parts.
typically, one H provides about 10^6 class of bent functions.
If I remember correctely the classification of H tooks two years
of research with Zanotti, Veron, and finaly 4 months of computations
on a single but good machine.
The classification tooks also two years with Leander, and 6 month
of computations involving 50-60 processors on network.
(2) The job is done. But it is not the only way to do it. One can
also start from the affine classification of semi-bent function in
7 variables (on my site) to discover all the bent in 8 variables.
I dont know the thesis. Since the very important papers of Hou on
the number of class of RM(k,m)/RM(s,m) are not in the references I
understand that probably the job of classification can not be a direct
consequence of her work.
