Geodesic
Enumeration of bent functions on the minimal distance from the quadratic bent function
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 1, pp. 41-58.

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Constructing bent functions on the minimal distance from the quadratic bent function is studied. All such bent functions in $2k$ variables are obtained and it is shown that the number of them is equal to $2^k(2^1+1)\dots(2^k+1)$. A lower bound of the number of bent functions on the minimal distance from a Maiorana–McFarland bent function is given. Tab. 1, bibliogr. 9.
Keywords: bent function, the minimal distance, quadratic bent function. 
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N. A. Kolomeec. Enumeration of bent functions on the minimal distance from the quadratic bent function. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 1, pp. 41-58. http://geodesic.mathdoc.fr/item/DA_2012_19_1_a3/

[1] Kolomeets N. A., Pavlov A. V., “Svoistva bent-funktsii, nakhodyaschikhsya na minimalnom rasstoyanii drug ot druga”, Prikl. diskret. matematika, 2009, no. 4, 5–20

[2] Logachev O. A., Salnikov A. A., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2004, 470 pp. | MR

[3] Mak-Vilyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979, 744 pp.

[4] Tokareva N. N., Nelineinye bulevy funktsii: bent-funktsii i ikh obobscheniya, Lambert Acad. Publ., Saarbrucken, Germany, 2011, 180 pp.

[5] Canteaut A., Daum M., Dobbertin H., Leander G., “Finding nonnormal bent functions”, Discrete Appl. Math., 154:2 (2006), 202–218 | DOI | MR | Zbl

[6] Carlet C., “Boolean functions for cryptography and error correcting codes”, Chapter of the monograph, Boolean methods and models (to appear) Prelim. version is available at http://www.math.univ-paris13.fr/~carlet/chap-fcts-Bool-corr.pdf

[7] Dillon J. F., “A survey of bent functions”, The NSA Techn. J., 1972, Special Issue, 191–215

[8] McFarland R. L., “A family of difference sets in non-cyclic groups”, J. Comb. Theory Ser. A, 15:1 (1973), 1–10 | DOI | MR | Zbl

[9] Rothaus O., “On bent functions”, J. Comb. Theory Ser. A, 20:3 (1976), 300–305 | DOI | MR | Zbl