Geodesic
Connections between quaternary and Boolean bent functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 73-75.

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This work is related to quaternary bent functions $f:\mathbb{Z}_4^n\rightarrow\mathbb{Z}_4$. The relation between Walsh — Hadamard transform coefficients of quaternary and two Boolean functions is explored. It is proved that any quaternary bent function is a regular bent function for any $n$. The number of quaternary bent functions in one and two variables is counted. For quaternary bent function in one variable $g(x+2y)=a(x,y)+2b(x,y)$, it is proved that $b$ and $a\oplus b$ are Boolean bent functions, where $x,y\in\mathbb{Z}_2$. Properties of Boolean functions $a,b$ and $a\oplus b$ in representation of quaternary bent function in two variables as $g(x+2y)=a(x,y)+2b(x,y)$ are described.
Keywords: quaternary functions, Boolean functions, regular bent functions. 
@article{PDMA_2019_12_a21,
     author = {A. S. Shaporenko},
     title = {Connections between quaternary and {Boolean} bent functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {73--75},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a21/}
}
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A. S. Shaporenko. Connections between quaternary and Boolean bent functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 73-75. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a21/

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