Geodesic
On some properties of known isometric mappings of the set of bent functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 43-44

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We prove that there doesn't exist an isometry on the set of all Boolean functions in $2k$ variables which acts on the set of bent functions by assigning the dual bent functions. We state the affine equivalence of a bent function and its dual bent function in the case of small number of variables.
Keywords: Boolean function, bent function, isometry, dual bent function. 
A. V. Kutsenko. On some properties of known isometric mappings of the set of bent functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 43-44. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a16/
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[1] Rothaus O., “On bent functions”, J. Combin. Theory Ser. A, 20:3 (1976), 300–305 | DOI | MR | Zbl

[2] Carlet C., Danielson L. E., Parker M. G., Solé P., “Self dual bent functions”, Int. J. Inform. Coding Theory, 1 (2010), 384–399 | DOI | MR | Zbl

[3] Carlet C., “Boolean functions for cryptography and error-correcting codes”, Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge Univ. Press, N.Y., 2010, 257–397 | DOI | Zbl

[4] Tokareva N. N., “Gruppa avtomorfizmov mnozhestva bent-funktsii”, Diskretnaya matematika, 22:4 (2010), 34–42 | DOI | MR | Zbl