On the Dual of Certain Ternary Weakly Regular Bent Functions

Author

Gong, Guang ; Helleseth, Tor ; Hu, Honggang ; Kholosha, Alexander

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada

Volume

58

Issue

4

fYear

2012

fDate

4/1/2012 12:00:00 AM

Firstpage

2237

Lastpage

2243

Abstract

In 2006, Helleseth and Kholosha conjectured and partially proved the existence of a class of ternary weakly regular monomial bent functions and also the expression for the dual bent function up to the sign value. The bentness was finally proved later in 2009 using a complicated technique that employs Stickelberger´s theorem. Extensively using the previously found results and approaches, in this paper, a surprisingly short proof for the conjectured expression of the dual is given but without resolving the sign ambiguity. Furthermore, we resolve the sign by finding the trace representation of the dual function.

Keywords

Boolean functions; Boolean bent function; Helleseth conjecture expression; Kholosha conjecture expression; Stickelberger theorem; dual bent function expression; dual function trace representation; ternary weakly regular monomial bent function; Computers; Educational institutions; Equations; Information theory; Lead; Mathematical model; Transforms; $p$-ary bent function; Gauss sum; Stickelberger\´s theorem; Walsh transform; weakly regular bent function;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2011.2176312

Filename

6082443