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

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

Jyrki Lahtonen 1, , Gary McGuire 2, and  Harold N. Ward 3,

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.
Keywords: quadratic form, Walsh-Hadamard transform, bent function..
Mathematics Subject Classification: 11T24, 94B1.
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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