Geodesic
On some measures of nonlinearity for Boolean functions
Prikladnaâ diskretnaâ matematika, no. 2 (2011), pp. 5-16

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A nonlinearity measure is defined for a Boolean function $f$ as a distance from $f$ to the set of algebraic degenerated functions. Relations between this measure and some early offered measures of the nonlinearity are considered. Also, we investigate the order of algebraic degeneration of those functions which are mostly close to $f$.
Keywords: nonlinearity of Boolean functions, algebraic degenerated functions, linear structures space, cryptography. 
@article{PDM_2011_2_a0,
     author = {E. K. Alekseev},
     title = {On some measures of nonlinearity for {Boolean} functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--16},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_2_a0/}
}
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E. K. Alekseev. On some measures of nonlinearity for Boolean functions. Prikladnaâ diskretnaâ matematika, no. 2 (2011), pp. 5-16. http://geodesic.mathdoc.fr/item/PDM_2011_2_a0/