Investigations on Bent and Negabent Functions via the Nega-Hadamard Transform
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 2012
- Accession Number
- ADA574590
Entities
People
- Aditi K. Gangopadhyay
- Ankita Chaturvedi
- Pantelimon Stanica
- Subhamoy Maitra
- Sugata Gangopadhyay
Organizations
- Naval Postgraduate School