The group of automorphisms of the set of bent functions
نویسندگان
چکیده
The bent functions are the Boolean functions of an even number of variables which are at the maximum possible distance from the set of all affine functions. In this paper, it is shown that each isometric mapping of the set of Boolean functions of n variables to itself preserving the class of bent functions is a combination of an affine transformation of coordinates and a shift by an affine function. It is proved that the affine functions are precisely all Boolean functions which are at the maximum possible distance from the class of bent functions. The research was supported by the Program of President of Russian Federation for support of young Russian scientists, grant 1250.2009.1; by the Russian Foundation for Basic Research, grants 08–01–00671, 09–01–00528, 10–01–00424; and by the Federal Program for support of scientific and pedagogical staff of innovational Russia for 2009–2013, state contract 02.740.11.0429.
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