Anbar Meidl, Nurdagül and Meidl, Wilfried and Pott, Alexander (2019) Equivalence for negabent functions and their relative difference sets. Discrete Applied Mathematics . ISSN 0166218X (Print) 18726771 (Online) Published Online First http://dx.doi.org/10.1016/j.dam.2019.07.018
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Official URL: http://dx.doi.org/10.1016/j.dam.2019.07.018
Abstract
A bent function from Fn 2 to F2, n even, can be transformed into a negabent function, or slightly more general into a bent4, also called shifted bent function, by adding a certain quadratic term. If n is odd, then negabent functions similarly correspond to semibent functions with some additional property. Whereas bent functions induce relative diﬀerence sets in Fn 2 ×F2, negabent functions induce relative diﬀerence sets in Fn−1 2 ×Z4. We analyse equivalence of negabent functions respectively of their relative diﬀerence sets. We show that equivalent bent functions can correspond to inequivalent negabent functions, hence one can obtain inequivalent relative diﬀerence sets in Fn−1 2 ×Z4 with EAequivalence. We also show that this is not the case when n is odd. Finally we analyse the class of semibent functions that corresponds to negabent functions and show that though partially bent semibent functions always can be shifted to negabent or bent4 functions, there are many semibent functions which do not correspond to negabent and bent4 functions.
Item Type:  Article 

Subjects:  Q Science > QA Mathematics > QA150272.5 Algebra 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Nurdagül Anbar Meidl 
Date Deposited:  04 Nov 2019 22:32 
Last Modified:  26 Apr 2022 10:12 
URI:  https://research.sabanciuniv.edu/id/eprint/39370 
Available Versions of this Item

Equivalence for negabent functions and their relative difference sets. (deposited 01 Aug 2019 22:36)
 Equivalence for negabent functions and their relative difference sets. (deposited 04 Nov 2019 22:32) [Currently Displayed]