On the dual of a Coulter-Matthews bent function

Coulter-Matthews (CM) bent functions are from F"3"^"n to F"3 defined by Tr(ax^1^2^(^3^^^@a^+^1^)), where a@?F"3"^"n^* and (@a,2n)=1. It is not known if these bent functions are weakly regular in general. In this paper, we show that when n is even and @a=n+1 (or n-1), the CM bent function is weakly regular. Moreover, we explicitly determine the dual of the CM bent function in this case. The dual is a bent function not reported previously.