Characterisation and enumeration of a class of semi bent quadratic Boolean functions

Koçak, Onur Ozan
Özbudak, Ferruh
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).
International Journal of Information and Coding Theory


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Citation Formats
N. KOÇAK, O. O. Koçak, F. Özbudak, and Z. SAYGI, “Characterisation and enumeration of a class of semi bent quadratic Boolean functions,” International Journal of Information and Coding Theory, pp. 39–57, 2015, Accessed: 00, 2020. [Online]. Available: