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Partial spread and vectorial generalized bent functions. (English) Zbl 1408.94997
Summary: In this paper we generalize the partial spread class and completely describe it for generalized Boolean functions from \({\mathbb {F}}_2^n\) to \({\mathbb {Z}}_{2^t}\). Explicitly, we describe gbent functions from \({\mathbb {F}}_2^n\) to \({\mathbb {Z}}_{2^t}\), which can be seen as a gbent version of Dillon’s \(PS_{ap}\) class. For the first time, we also introduce the concept of a vectorial gbent function from \({\mathbb {F}}_2^n\) to \({\mathbb {Z}}_q^m\), and determine the maximal value which \(m\) can attain for the case \(q=2^t\). Finally we point to a relation between vectorial gbent functions and relative difference sets.

MSC:
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
06E30 Boolean functions
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
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