Non-existence results for vectorial bent functions with Dillon exponent

Abstract

We prove new non-existence results for vectorial monomial Dillon type bent functions mapping the field of order 2 2 m 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.