Geodesic
Functions without short implicents.Part I: lower estimates of weights
Diskretnaya Matematika, Tome 27 (2015) no. 2, pp. 94-105

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The paper is concerned with $n$-place Boolean functions not admitting implicents of $k$ variables, $1\le k$. Estimates for the minimal possible weight $w\left( {n,\;k} \right)$ of such functions are obtained. It is shown that $w\left( {n,\;1} \right) = 2$, $n = 2,3,...$, and $w\left( {n,\;2} \right)\sim{\log _2}n$ as $n \to \infty$, and moreover, for $k > 2$ there exists ${n_0}$ such that $w\left( {n,\;k} \right) > {2^{k - 2}} \cdot {\log _2}n$ for all $n > {n_0}$.
Keywords: Boolean function, implicent, combinatorially complete matrix. 
@article{DM_2015_27_2_a5,
     author = {Pavel V. Roldugin and Alexey V. Tarasov},
     title = {Functions without short {implicents.Part} {I:} lower estimates of weights},
     journal = {Diskretnaya Matematika},
     pages = {94--105},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_2_a5/}
}
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Pavel V. Roldugin; Alexey V. Tarasov. Functions without short implicents.Part I: lower estimates of weights. Diskretnaya Matematika, Tome 27 (2015) no. 2, pp. 94-105. http://geodesic.mathdoc.fr/item/DM_2015_27_2_a5/