Characterisation and enumeration of a class of semi-bent quadratic Boolean functions
Summary: 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 [\textit{W. Ma} et al., IEICE Trans. Fundam. E-88-A, No. 7, 2039--2040 (2005)].
scientific article; zbMATH DE number 6537524
scientific article