Gold and Kasami-Welch functions, quadratic forms, and bent functions
Jyrki Lahtonen, Gary McGuire, Harold N. Ward · Advances in Mathematics of Communications · 2007
We use elementary facts about quadratic forms in characteristic 2 to evaluate the sign of some Walsh transforms in terms of a Jacobi symbol. These results are applied to the Walsh transforms of the Gold and Kasami-Welch functions. We prove that the Gold functions yield bent functions when restricted to certain hyperplanes. We also use the sign information to determine the dual bent function.