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Mathematical Problems in Engineering
Volume 2015, Article ID 959617, 8 pages
Research Article

On Negabent Functions and Nega-Hadamard Transform

School of Mathematical Science, Huaibei Normal University, Huaibei, Anhui 235000, China

Received 29 June 2015; Revised 23 October 2015; Accepted 26 October 2015

Academic Editor: Laura Gardini

Copyright © 2015 Zepeng Zhuo and Jinfeng Chong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 which is negabent function. Based on them, the construction for generating the negabent functions by concatenation is given. Finally, the function expressed as is discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained.