On Negabent Functions and Nega-Hadamard Transform

摘要

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, neg-aautocorrelation coefficients, sum-of-squares indicators, and so on. We establish a new equivalent statement on f(1) parallel to f(2) 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 circle plus a)circle plus b.x circle plus c is discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained.