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Designs, Codes and Cryptography

Erschienen in:

08.10.2016

Partial spread and vectorial generalized bent functions

verfasst von: Thor Martinsen, Wilfried Meidl, Pantelimon Stănică

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2017

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Abstract

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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Titel: Partial spread and vectorial generalized bent functions
verfasst von: Thor Martinsen
Wilfried Meidl
Pantelimon Stănică
Publikationsdatum: 08.10.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2017
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-016-0283-7

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