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Self-dual bent functions. (English) Zbl 1204.94118
Summary: A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterisation in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of the Sylvester matrix is derived. Primary and secondary constructions are given. All self-dual bent Boolean functions in $$\leq 6$$ variables and all quadratic such functions in eight variables are given, up to a restricted form of affine equivalence.

MSC:
 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010) 06E30 Boolean functions
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