Geodesic
Nonlinearity bounds for vectorial Boolean functions of special form
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 24-26

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The problem of combining different cryptographic properties of vectorial Boolean functions is considered. An upper nonlinearity bound for vectorial Boolean functions constructed using affine Boolean functions is obtained. It is shown that, for any natural $n$, the bound is reachable. Besides, a lower bound for the number of vectorial functions having a fixed nonlinearity and constructed from balanced Boolean functions is obtained.
Keywords: vectorial Boolean function, nonlinearity, affine function, balancedness. 
@article{PDMA_2014_7_a8,
     author = {E. P. Korsakova},
     title = {Nonlinearity bounds for vectorial {Boolean} functions of special form},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {24--26},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a8/}
}
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E. P. Korsakova. Nonlinearity bounds for vectorial Boolean functions of special form. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 24-26. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a8/