Non-existence results for vectorial bent functions with Dillon exponent.

Discrete Applied Mathematics 316 (2022), 71-74.

We prove new non-existence results for vectorial monomial Dillon type bent functions mapping the field of order 2^{2m} to the field of order 2^{m/3}. When m is odd and m>3 we show that there are no such functions. When m is even we derive a condition for the bent coefficient. The latter result allows us to find examples of bent functions with m=6 in a simple way.