## 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⩾ 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 language | English |
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Pages (from-to) | 201-222 |

Number of pages | 22 |

Journal | Designs, Codes, and Cryptography |

Volume | 88 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2020 |

## Keywords

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