Proofs of two conjectures on ternary weakly regular bent functions

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dc.creatorHelleseth, Tor
dc.creatorHollmann, Henk D. L.
dc.creatorKholosha, Alexander
dc.creatorWang, Zeying
dc.creatorXiang, Qing
dc.date2008-03-19
dc.date.accessioned2026-07-07T09:27:36Z
dc.date.available2026-07-07T09:27:36Z
dc.descriptionWe 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.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0803.2878
dc.identifierhttp://arxiv.org/abs/0803.2878
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157160
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject11T71; 05B99
dc.titleProofs of two conjectures on ternary weakly regular bent functions
dc.typetext

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