Investigations on Bent and Negabent Functions via the Nega-Hadamard Transform
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
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Parker et al. considered a new type of discrete Fourier transform, called nega-Hadamard transform. We prove several results regarding its behavior on combinations of Boolean functions and use this theory to derive several results on negabentness that is, flat nega-spectrum of concatenations, and partially symmetric functions. We derive the upper bound for the algebraic degree of a negabent function on variables. Further, a characterization of bent-negabent functions is obtained within a subclass of the Maiorana-McFarland set. We develop a technique to construct bent-negabent Boolean functions by using complete mapping polynomials. Using this technique, we demonstrate that for each there exist bent-negabent functions on variables with algebraic degree . It is also demonstrated that there exist bent-negabent functions on eight variables with algebraic degrees 2, 3, and 4. Simple proofs of several previously known facts are obtained as immediate consequences of our work.
- Numerical Mathematics