Metrical properties of self-dual bent functions

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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⩾ 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⩾ 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.

Original languageEnglish
Pages (from-to)201-222
Number of pages22
JournalDesigns, Codes, and Cryptography
Issue number1
Publication statusPublished - 1 Jan 2020


  • Boolean functions
  • Iterative construction
  • Metrical regularity
  • Self-dual bent


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