Root-Hadamard transforms and complementary sequences

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Authors
Medina, Luis A.
Parker, Matthew G.
Riera, Constanza
Stănică, Pantelimon
Subjects
Golay pairs
Boolean functions
correlations
Generalized transforms
Advisors
Date of Issue
2019-07
Date
Publisher
Springer
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Abstract
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.
Type
Article
Description
The article of record as published may be found at https://doi.org/10.1007/s12095-020-00440-4
URI
https://hdl.handle.net/10945/65339
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Department
Applied Mathematics
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Format
15 p.
Citation
Medina, Luis A., et al. "Root-Hadamard transforms and complementary sequences." Cryptography and Communications (2020): 1-15.
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This 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.
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