Characterisation and enumeration of a class of semi-bent quadratic Boolean functions
by Neşe Koçak; Onur Koçak; Ferruh Özbudak; Zülfükar Saygı
International Journal of Information and Coding Theory (IJICOT), Vol. 3, No. 1, 2015

Abstract: In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous partial and incomplete enumeration results for three other classes of semi-bent/bent functions in the literature using this method. We also correct some results on quadratic bent functions stated in Ma et al. (2005).

Online publication date: Thu, 09-Apr-2015

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