On vectorial bent functions with Dillon-type exponents.

Proceedings of 2016 IEEE International Symposium on Information Theory (ISIT 2016), Barcelona, Spain, July 2016, pp. 490-494.

We study vectorial bent functions with Dillon-type exponents. These functions have attracted attention because they are hyperbent whenever they are bent, and they achieve the highest possible algebraic degree among all bent functions on the same domain. In low dimensions we determine the simplest possible forms of such functions when they map to GF(4). We prove non-existence results for certain monomial and multinomial bent functions mapping to large codomains.