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arXiv · 1907.09360

Root-Hadamard transforms and complementary sequences

Luis A. Medina·Matthew G. Parker·Constanza Riera·Pantelimon Stanica
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Abstract

In this paper we define a new transform on (generalized) Boolean functions, which generalizes the Walsh-Hadamard, nega-Hadamard, $2^k$-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.

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Luis A. Medina, Matthew G. Parker, Constanza Riera, Pantelimon Stanica. 2019-07-22. Root-Hadamard transforms and complementary sequences. https://arxiv.org/abs/1907.09360

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