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Kasami bent functions are not equivalent to their duals. (English) Zbl 1173.94468
Mullen, Gary L. (ed.) et al., Finite fields and applications. Proceedings of the eighth international conference on finite fields and applications, Melbourne, Australia, July 9–13, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4309-3/pbk). Contemporary Mathematics 461, 187-197 (2008).
Summary: A difficult task in the theory of bent functions is to determine whether a bent function is equivalent to its dual bent function. We find the degree of the dual bent function of the Kasami monomial bent function, which in general is different from the degree of the Kasami function itself. It follows that the Kasami bent functions are not equivalent to their duals in general.
For the entire collection see [Zbl 1141.11002].

94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
11T06 Polynomials over finite fields
12E20 Finite fields (field-theoretic aspects)