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Advances in Mathematics of Communications (AMC)
 

On the dual of (non)-weakly regular bent functions and self-dual bent functions

Pages: 425 - 440, Volume 7, Issue 4, November 2013      doi:10.3934/amc.2013.7.425

 
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Ayça Çeşmelioǧlu - Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106, Magdeburg, Germany (email)
Wilfried Meidl - MDBF, Sabanci University, Orhanlı, Tuzla 34956, İstanbul, Turkey (email)
Alexander Pott - Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106, Magdeburg, Germany (email)

Abstract: For weakly regular bent functions in odd characteristic the dual function is also bent. We analyse a recently introduced construction of non-weakly regular bent functions and show conditions under which their dual is bent as well. This leads to the definition of the class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass. We analyse self-duality for bent functions in odd characteristic, and characterize quadratic self-dual bent functions. We construct non-weakly regular bent functions with and without a bent dual, and bent functions with a dual bent function of a different algebraic degree.

Keywords:  Duals of bent functions, self-dual bent functions, Fourier transform.
Mathematics Subject Classification:  Primary: 11T71, 94A60, 06E30; Secondary: 11T24.

Received: July 2012;      Revised: March 2013;      Available Online: October 2013.

 References