Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices
Combinatorics
2022-07-13 v1
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.
Cite
@article{arxiv.2207.05735,
title = {Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices},
author = {José Andrés Armario and Ronan Egan and Dane Flannery},
journal= {arXiv preprint arXiv:2207.05735},
year = {2022}
}