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arXiv · 0803.2878

Proofs of two conjectures on ternary weakly regular bent functions

Tor Helleseth·Henk D. L. Hollmann·Alexander Kholosha·Zeying Wang·Qing Xiang
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Abstract

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.

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Tor Helleseth, Henk D. L. Hollmann, Alexander Kholosha, Zeying Wang, Qing Xiang. 2008-03-19. Proofs of two conjectures on ternary weakly regular bent functions. https://arxiv.org/abs/0803.2878

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