Geodesic
On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation
Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 14-24

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We find a relation between the $W$-intersection matrix (which characterizes the degree of “nonhomomorphy”) of a transformation and the difference distribution table and the correlation matrix (which characterize the degree nonlinearity of a transformation). An upper estimate for the dimension of a subspace invariant under almost bent functions is put forward. A formula for evaluation of the $W$-intersection matrix of a composition of two transformations is obtained.
Keywords: $W$-intersection matrix, correlation matrix, difference distribution table, differential attack, linear attack. 
@article{DM_2018_30_3_a1,
     author = {D. A. Burov},
     title = {On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation},
     journal = {Diskretnaya Matematika},
     pages = {14--24},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_3_a1/}
}
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D. A. Burov. On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation. Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 14-24. http://geodesic.mathdoc.fr/item/DM_2018_30_3_a1/