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arXiv · 2207.05735

Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices

José Andrés Armario·Ronan Egan·Dane Flannery
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Abstract

In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering Butson matrices that are cocyclic rather than strictly group invariant. This result has several applications; for example, to the construction of Boolean functions whose expansions are generalized partially bent functions, including cases where no bent function can exist.

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José Andrés Armario, Ronan Egan, Dane Flannery. 2022-07-12. Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices. https://arxiv.org/abs/2207.05735

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