Abstract
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 \(n\geqslant 4\) 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 \(n\geqslant 4\) 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.
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Communicated by C. Carlet.
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The author was supported by the Russian Foundation for Basic Research (Projects No. 18-31-00374, 18-07-01394), by the Ministry of Education and Science of the Russian Federation (the 5-100 Excellence Programme and the Project No. 1.12875.2018/12.1), by the program of fundamental scientific researches of the SB RAS No. I.5.1. (Project No. 0314-2016-0017).
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Kutsenko, A. Metrical properties of self-dual bent functions. Des. Codes Cryptogr. 88, 201–222 (2020). https://doi.org/10.1007/s10623-019-00678-x
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DOI: https://doi.org/10.1007/s10623-019-00678-x