Geodesic
On the affine classification of cubic bent functions
Trudy Instituta matematiki, Tome 14 (2006) no. 1, pp. 3-11 
S. V. Agievich. On the affine classification of cubic bent functions. Trudy Instituta matematiki, Tome 14 (2006) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/TIMB_2006_14_1_a0/
@article{TIMB_2006_14_1_a0,
     author = {S. V. Agievich},
     title = {On the affine classification of cubic bent functions},
     journal = {Trudy Instituta matematiki},
     pages = {3--11},
     year = {2006},
     volume = {14},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2006_14_1_a0/}
}
TY  - JOUR
AU  - S. V. Agievich
TI  - On the affine classification of cubic bent functions
JO  - Trudy Instituta matematiki
PY  - 2006
SP  - 3
EP  - 11
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2006_14_1_a0/
LA  - ru
ID  - TIMB_2006_14_1_a0
ER  - 
%0 Journal Article
%A S. V. Agievich
%T On the affine classification of cubic bent functions
%J Trudy Instituta matematiki
%D 2006
%P 3-11
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2006_14_1_a0/
%G ru
%F TIMB_2006_14_1_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider cubic boolean bent functions, each cubic monomials of which contain the same variable. We investigate canonical forms of these functions under affine transformations of variables. In particular, we refine the affine classification of cubic bent functions of $8$ variables.

[1] Rothaus O.S., “On bent functions”, J. Comb. Theory. Ser. A, 20 (1979), 300–305 | DOI | MR

[2] Mak-Vilyams M.Dzh., Sloen N.Dzh.A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979

[3] Hou X., “Cubic bent functions”, Discrete Math., 89 (1998), 149–161 | DOI | MR

[4] Cheremushkin A.V., “Metody affinnoi i lineinoi klassifikatsii dvoichnykh funktsii”, Tr. po diskretnoi matematike, 4, Fizmatlit, M., 2001, 273–314

[5] Hou X., “$GL(m,2)$ acting on $R(r,m)/R(r-1,m)$”, Discrete Math., 149 (1996), 99–122 | DOI | MR | Zbl

[6] Agievich S., “On the representation of bent functions by bent rectangles”, Probabilistic Methods in Discrete Mathematics, Proceedings of the Fifth International Petrozavodsk Conference (Petrozavodsk, June 1–6, 2000), VSP, Utrecht, Boston, 2002, 121–135

[7] Gantmakher F.R., Teoriya matrits, Nauka, M., 1988 | MR | Zbl