Geodesic
Symmetric Boolean functions and their metric properties matrices of transitions of differences when using some modular groups
Matematičeskie voprosy kriptografii, Tome 4 (2013), pp. 49-63.

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Various metric properties of symmetric Boolean functions are analysed (including the case of random functions). The minimal and maximal distances from a given Boolean function to the set of symmetric functions (as well to its subsets) are found. The structure and the size of the set of functions which are the farthest from the symmetric functions set are investigated. 
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G. I. Ivchenko; Yu. I. Medvedev; V. A. Mironova. Symmetric Boolean functions and their metric properties matrices of transitions of differences when using some modular groups. Matematičeskie voprosy kriptografii, Tome 4 (2013), pp. 49-63. http://geodesic.mathdoc.fr/item/MVK_2013_4_a3/

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