# American Institute of Mathematical Sciences

May  2007, 1(2): 243-250. doi: 10.3934/amc.2007.1.243

## Gold and Kasami-Welch functions, quadratic forms, and bent functions

 1 Department of Mathematics, University of Turku, 20014 Turku, Finland 2 School of Mathematical Sciences, University College Dublin, Dublin 4, Ireland 3 Department of Mathematics, University of Virginia, Charlottesville, VA 22904, United States

Received  December 2006 Revised  March 2007 Published  May 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.
Citation: Jyrki Lahtonen, Gary McGuire, Harold N. Ward. Gold and Kasami-Welch functions, quadratic forms, and bent functions. Advances in Mathematics of Communications, 2007, 1 (2) : 243-250. doi: 10.3934/amc.2007.1.243
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