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Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices
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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 equivalencesby 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.Mathematics Subject Classification (2010) 15B34 · 05B20 · 94D05
Title: Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices
Description:
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 equivalencesby 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.
Mathematics Subject Classification (2010) 15B34 · 05B20 · 94D05.
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