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

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  • 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.
    Mathematics Subject Classification: 11T24, 94B15.

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