179 research outputs found
Proofs of two conjectures on ternary weakly regular bent functions
We study ternary monomial functions of the form f(x)=\Tr_n(ax^d), where
x\in \Ff_{3^n} and \Tr_n: \Ff_{3^n}\to \Ff_3 is the absolute trace
function. Using a lemma of Hou \cite{hou}, Stickelberger's theorem on Gauss
sums, and certain ternary weight inequalities, we show that certain ternary
monomial functions arising from \cite{hk1} are weakly regular bent, settling a
conjecture of Helleseth and Kholosha \cite{hk1}. We also prove that the
Coulter-Matthews bent functions are weakly regular.Comment: 20 page
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