New monomial bent functions over the finite fields of odd characteristic

@article{Helleseth2005NewMB,
  title={New monomial bent functions over the finite fields of odd characteristic},
  author={Tor Helleseth and Alexander Kholosha},
  journal={IEEE Information Theory Workshop, 2005.},
  year={2005},
  pages={5 pp.-}
}
We consider p-ary bent functions having the form f(x) = Tr/sub n/ (ax/sup d/). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. We also discuss the (weak) regularity of our new… CONTINUE READING