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Metrical properties of self-dual bent functions. (English) Zbl 07149379
Summary: In this paper we study metrical properties of Boolean bent functions which coincide with their dual bent functions. We propose an iterative construction of self-dual bent functions in $$n+2$$ variables through concatenation of two self-dual and two anti-self-dual bent functions in $$n$$ variables. We prove that minimal Hamming distance between self-dual bent functions in $$n$$ variables is equal to $$2^{n/2}$$. It is proved that within the set of sign functions of self-dual bent functions in $$n\geq 4$$ variables there exists a basis of the eigenspace of the Sylvester Hadamard matrix attached to the eigenvalue $$2^{n/2}$$. Based on this result we prove that the sets of self-dual and anti-self-dual bent functions in $$n\geq 4$$ variables are mutually maximally distant. It is proved that the sets of self-dual and anti-self-dual bent functions in $$n$$ variables are metrically regular sets.

MSC:
 06E30 Boolean functions 15B34 Boolean and Hadamard matrices 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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References:
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