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Cryptography and Communications
Published in: Cryptography and Communications 5/2020

22-06-2020

Root-Hadamard transforms and complementary sequences

Authors: Luis A. Medina, Matthew G. Parker, Constanza Riera, Pantelimon Stănică

Published in: Cryptography and Communications | Issue 5/2020

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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.
previous article Combinatorial t-designs from special functions
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Metadata
Title
Root-Hadamard transforms and complementary sequences
Authors
Luis A. Medina
Matthew G. Parker
Constanza Riera
Pantelimon Stănică
Publication date
22-06-2020
Publisher
Springer US
Published in
Cryptography and Communications / Issue 5/2020
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-020-00440-4

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