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. 
@article{PDMA_2017_10_a16,
     author = {A. V. Kutsenko},
     title = {On some properties of known isometric mappings of the set of bent functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {43--44},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a16/}
}
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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/