Geodesic
Characterization of generalized bent functions of algebraic degree $1$
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 37-40

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Bent functions of the form $\mathbb{F}_2^n\rightarrow\mathbb{Z}_q$, where $q\geqslant2$ is a positive integer, are known as generalized bent (gbent) functions. A gbent function for which it is possible to define a dual gbent function is called regular. We study gbent functions of degree $1$. Criterion of the generalized Boolean function of degree $1$ to be gbent is obtained. The conditions under which the function is regular or weakly regular are described. Component Boolean functions are investigated, it follows that for the case $q=2^k$ two of them, having maximal indices, are quadratic, while the rest are constant.
Keywords: generalized bent function, regular gbent function, affine function, component Boolean function. 
@article{PDMA_2024_17_a8,
     author = {A. V. Kutsenko},
     title = {Characterization of generalized bent functions of algebraic degree $1$},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {37--40},
     publisher = {mathdoc},
     number = {17},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2024_17_a8/}
}
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A. V. Kutsenko. Characterization of generalized bent functions of algebraic degree $1$. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 37-40. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a8/