DocumentCode :
1377800
Title :
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
Link To Document :
بازگشت