On Negabent Functions and Nega-Hadamard Transform

The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called negabent function. In this paper, the special Boolean functions by concatenation are presented. We investigate their nega-Hadamard transforms, nega-autocorrelation coefficients, sum-of-squares indicators, and so on. We establish a new equivalent statement on f1∥f2 which is negabent function. Based on them, the construction for generating the negabent functions by concatenation is given. Finally, the function expressed as f(Ax⊕a)⊕b·x⊕c is discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained.