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

Jyrki Lahtonen | Zendy; Gary McGuire | Zendy; Harold N. Ward | Zendy

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

Author(s) -

Jyrki Lahtonen,

Gary McGuire,

Harold N. Ward

Publication year - 2007

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2007.1.243

Subject(s) - mathematics , bent molecular geometry , bent function , sign (mathematics) , hyperplane , quadratic equation , symbol (formal) , function (biology) , sign function , combinatorics , boolean function , quadratic function , pure mathematics , discrete mathematics , arithmetic , mathematical analysis , geometry , computer science , chemistry , organic chemistry , evolutionary biology , biology , programming language

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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