Geodesic
Boolean functions as points on the hypersphere in the Euclidean space
Diskretnaya Matematika, Tome 30 (2018) no. 1, pp. 39-55

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A new approach to the study of algebraic, combinatorial, and cryptographic properties of Boolean functions is proposed. New relations between functions have been revealed by consideration of an injective mapping of the set of Boolean functions onto the sphere in a Euclidean space. Moreover, under this mapping some classes of functions have extremely regular localizations on the sphere. We introduce the concept of curvature of a Boolean function, which characterizes its proximity (in some sense) to maximally nonlinear functions.
Keywords: Boolean function, Hamming space, Euclidean space, multidimensional sphere, Fourier (Walsh–Hadamard) transform, maximal nonlinearity, bent function. 
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     author = {O. A. Logachev and S. N. Fedorov and V. V. Yashchenko},
     title = {Boolean functions as points on the hypersphere in the {Euclidean} space},
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O. A. Logachev; S. N. Fedorov; V. V. Yashchenko. Boolean functions as points on the hypersphere in the Euclidean space. Diskretnaya Matematika, Tome 30 (2018) no. 1, pp. 39-55. http://geodesic.mathdoc.fr/item/DM_2018_30_1_a2/