In the class of invertible vectorial Boolean functions in $n$ variables with coordinate functions depending on all variables, we consider the subclasses $\mathcal{K}_{n}$ and $\mathcal{K}'_{n}$, the functions in which are obtained using $n$ independent transpositions, respectively, from the identity permutation and from the permutation, each coordinate function of which essentially depends on some one variable. It is shown that, for any $F=(f_1\ldots f_n)\in\mathcal{K}_{n}\cup\mathcal{K}'_{n}$ and $i=1,\ldots,n$, the coordinate function $f_i$ has a single linear variable, the component function $vF$ has no nonessential and linear variables for each vector $v\in{\mathbb F}_2^n$ weight of which is greater than $1$, the nonlinearity, the degree, and the component algebraic immunity are $2$, $n-1$, and $2$ respectively.
I. A. Pankratova. About the components of some classes of invertible vectorial Boolean functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 66-68. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a19/
@article{PDMA_2019_12_a19,
author = {I. A. Pankratova},
title = {About the components of some classes of invertible vectorial {Boolean} functions},
journal = {Prikladnaya Diskretnaya Matematika. Supplement},
pages = {66--68},
year = {2019},
number = {12},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a19/}
}
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AU - I. A. Pankratova
TI - About the components of some classes of invertible vectorial Boolean functions
JO - Prikladnaya Diskretnaya Matematika. Supplement
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UR - http://geodesic.mathdoc.fr/item/PDMA_2019_12_a19/
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[4] Pankratova I. A., “Svoistva komponent nekotorykh klassov vektornykh bulevykh funktsii”, Prikladnaya diskretnaya matematika, 2019, no. 44, 5–11
