63 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
Strongly Regular Graphs Constructed from -ary Bent Functions
In this paper, we generalize the construction of strongly regular graphs in
[Y. Tan et al., Strongly regular graphs associated with ternary bent functions,
J. Combin.Theory Ser. A (2010), 117, 668-682] from ternary bent functions to
-ary bent functions, where is an odd prime. We obtain strongly regular
graphs with three types of parameters. Using certain non-quadratic -ary bent
functions, our constructions can give rise to new strongly regular graphs for
small parameters.Comment: to appear in Journal of Algebraic Combinatoric
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