an:07149379
Zbl 07149379
Kutsenko, Aleksandr
Metrical properties of self-dual bent functions
EN
Des. Codes Cryptography 88, No. 1, 201-222 (2020).
00443787
2020
j
06E30 15B34 94C10
Boolean functions; self-dual bent; iterative construction; metrical regularity
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.
Reviewer (Berlin)