Root-Hadamard transforms and complementary sequences
Medina, Luis A.
Parker, Matthew G.
MetadataShow full item record
In this paper we define a new transform on (generalized) Boolean functions, which generalizes the Walsh-Hadamard, nega-Hadamard, 2k-Hadamard, consta-Hadamard and all HN-transforms. We describe the behavior of what we call the root-Hadamard transform for a generalized Boolean function f in terms of the binary components of f. Further, we define a notion of complementarity (in the spirit of the Golay sequences) with respect to this transform and furthermore, we describe the complementarity of a generalized Boolean set with respect to the binary components of the elements of that set.
The article of record as published may be found at https://doi.org/10.1007/s12095-020-00440-4
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
Correlation immunity, avalanche features, and other cryptographic properties of generalized Boolean functions Martinsen, Thor (Monterey, California: Naval Postgraduate School, 2017-09);This dissertation investigates correlation immunity, avalanche features, and the bent cryptographic properties for generalized Boolean functions defined on Vn with values in Zԛ. We extend the concept of correlation immunity ...
Gangopadhyay, Sugata; Gangopadhyay, Aditi Kar; Pollatos, Spyridon; Stănică, Pantelimon (2015-07-31);While performing cryptanalysis, it is of interest to approximate a Boolean function in n variables f : Fn → F2 by affine functions. Usually, it is assumed that all the input vectors to a Boolean function are equiprobable ...
Gangopadhyay, Sugata; Pasalic, Enes; Stănică, Pantelimon (2012);In this paper, we consider the spectra of Boolean functions with respect to the action of unitary transforms obtained by taking tensor products of the Hadamard kernel, denoted by H, and the nega–Hadamard kernel, denoted ...