Accession Number:

ADA574590

Title:

Investigations on Bent and Negabent Functions via the Nega-Hadamard Transform

Descriptive Note:

Journal article

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS

Report Date:

2012-06-01

Pagination or Media Count:

10.0

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.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE