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08.10.2016 | Ausgabe 1/2017

Designs, Codes and Cryptography 1/2017

Partial spread and vectorial generalized bent functions

Designs, Codes and Cryptography > Ausgabe 1/2017
Thor Martinsen, Wilfried Meidl, Pantelimon Stănică
Wichtige Hinweise
Communicated by J. D. Key.


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.

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