Geodesic
On some properties of self-dual bent functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 44-46

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We study the properties of self-dual bent functions. It is proved that the minimal Hamming distance between self-dual bent functions is $2^{n/2}$ and the set of self-dual bent functions is a metrically regular set. The necessary and sufficient conditions for the iterative bent functions $\mathcal{BI}$ (A. Canteaut, P. Charpin, 2003) to be self-dual bent have been found. We have proved that there exists a self-dual bent function in $n$ variables and of any degree $d\in\{2,3,\dots,n/2\}$.
Keywords: Boolean function, bent function, iterative construction of bent functions, self-dual bent, metrically regular set. 
@article{PDMA_2018_11_a12,
     author = {A. V. Kutsenko},
     title = {On some properties of self-dual bent functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {44--46},
     publisher = {mathdoc},
     number = {11},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2018_11_a12/}
}
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A. V. Kutsenko. On some properties of self-dual bent functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 44-46. http://geodesic.mathdoc.fr/item/PDMA_2018_11_a12/