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
fDate :
4/1/2012 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2176312