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

Jyrki Lahtonen; Gary McGuire; Harold N. Ward

doi:10.3934/amc.2007.1.243

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2007, Volume 1, Issue 2: 243-250. Doi: 10.3934/amc.2007.1.243

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

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

Received: November 30, 2006

Revised: February 28, 2007

Published: June 2007

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Abstract

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.

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Mathematics Subject Classification: 11T24, 94B15.

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