Article ID Journal Published Year Pages File Type
420873 Discrete Applied Mathematics 2006 17 Pages PDF
Abstract

The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n   variables is called normal if there exists an affine subspace of dimension n/2n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in [J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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