Planar Functions and Planes of Lenz-Barlotti Class II
Designs, Codes and Cryptography
Monomial and quadratic bent functions over the finite fields of odd characteristic
IEEE Transactions on Information Theory
p-Ary and q-ary versions of certain results about bent functions and resilient functions
Finite Fields and Their Applications
Proofs of two conjectures on ternary weakly regular bent functions
IEEE Transactions on Information Theory
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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.