Geodesic
Investigation of some subclasses of multiaffine, bijunctive, weakly positive and weakly negative Boolean functions
Matematičeskie voprosy kriptografii, Tome 7 (2016), pp. 51-66

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Sets of multiaffine (denoted by $A$), bijunctive ($2$-CNF, $Bi$), weakly positive (or anti-Horn, $WP$) and weakly negative (or Horn, $WN$) Boolean functions generate classes of polynomially solvable systems of equations. We investigate functional classes $A\cap B$, $Bi\cap B$, where $B$ is the set of bent functions. Sets of possible values of algebraic nonlinearity degree of functions from $A$, $Bi$, $WP$, $WN$ are described. Problems of construction of functions from classes $WP$, $WN$ by means of functions of smaller number of variables are considered. 
@article{MVK_2016_7_a3,
     author = {S. P. Gorshkov},
     title = {Investigation of some subclasses of multiaffine, bijunctive, weakly positive and weakly negative {Boolean} functions},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {51--66},
     publisher = {mathdoc},
     volume = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2016_7_a3/}
}
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S. P. Gorshkov. Investigation of some subclasses of multiaffine, bijunctive, weakly positive and weakly negative Boolean functions. Matematičeskie voprosy kriptografii, Tome 7 (2016), pp. 51-66. http://geodesic.mathdoc.fr/item/MVK_2016_7_a3/