Geodesic
Isometric mappings of the set of all Boolean functions into itself which preserve self-duality and the Rayleigh quotient
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 55-58

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In the paper, we study isometric mappings of the set of all Boolean functions in $n$ variables into itself which preserve self-duality and the Rayleigh quotient of Boolean function and generalize known results. It is proved that isometric mapping preserves self-duality if and only if it preserves anti-self-duality. The complete characterization of these mappings is obtained. Based on this result, the set of isometric mappings which preserve the Rayleigh quotient of a Boolean function is described. As a corollary, all isometric mappings which preserve bentness and the Hamming distance between bent function and its dual are given.
Keywords: Boolean function, isometric mapping, self-dual bent function, Rayleigh quotient. 
@article{PDMA_2019_12_a15,
     author = {A. V. Kutsenko},
     title = {Isometric mappings of the set of all {Boolean} functions into itself which preserve self-duality and the {Rayleigh} quotient},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {55--58},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a15/}
}
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A. V. Kutsenko. Isometric mappings of the set of all Boolean functions into itself which preserve self-duality and the Rayleigh quotient. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 55-58. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a15/