Geodesic
On decomposition of bent functions in $8$ variables into the sum of two bent functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 40-42

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A Boolean function in an even number of variables is called bent if it has maximal nonlinearity. We study the well-known hypothesis about the representation of arbitrary Boolean functions in $n$ variables of degree at most $n/2$ as the sum of two bent functions. We prove that bent functions in $8$ variables of degree at most $3$ can be represented as the sum of two bent functions in $8$ variables. It was shown that all quadratic Boolean functions in an even number of variables $n\geqslant 4$ can be represented as the sum of two bent functions of a special form.
Keywords: Boolean functions, bent functions, decomposition into sum of bent functions. 
@article{PDMA_2022_15_a9,
     author = {A. S. Shaporenko},
     title = {On decomposition of bent functions in $8$ variables into the sum of two bent functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {40--42},
     publisher = {mathdoc},
     number = {15},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2022_15_a9/}
}
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A. S. Shaporenko. On decomposition of bent functions in $8$ variables into the sum of two bent functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 40-42. http://geodesic.mathdoc.fr/item/PDMA_2022_15_a9/