New Classes of Ternary Bent Functions from the Coulter-Matthews Bent Functions

It has been an active research issue for many years to construct new bent functions. For k odd with gcd(n, k) = 1, and a ∈ F3n , the function f(x) = Tr(ax 3k+1 2 ) is weakly regular bent over F3n , where Tr(·) : F3n → F3 is the trace function. This is the well-known Coulter-Matthews bent function. In this paper, we determine the dual function of f(x) completely. As a consequence, we find many classes of ternary bent functions not reported in the literature previously. Such bent functions are not quadratic if k > 1, and have (