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Metrical properties of self-dual bent functions. / Kutsenko, Aleksandr.

In: Designs, Codes, and Cryptography, Vol. 88, No. 1, 01.01.2020, p. 201-222.

Research output: Contribution to journal › Article › peer-review

Harvard

Kutsenko, A 2020, 'Metrical properties of self-dual bent functions', Designs, Codes, and Cryptography, vol. 88, no. 1, pp. 201-222. https://doi.org/10.1007/s10623-019-00678-x

APA

Kutsenko, A. (2020). Metrical properties of self-dual bent functions. Designs, Codes, and Cryptography, 88(1), 201-222. https://doi.org/10.1007/s10623-019-00678-x

Vancouver

Kutsenko A. Metrical properties of self-dual bent functions. Designs, Codes, and Cryptography. 2020 Jan 1;88(1):201-222. doi: 10.1007/s10623-019-00678-x

Author

Kutsenko, Aleksandr. / Metrical properties of self-dual bent functions. In: Designs, Codes, and Cryptography. 2020 ; Vol. 88, No. 1. pp. 201-222.

BibTeX

@article{a42e7dabb3be4d4eacdcf6f1223f4e0e,
title = "Metrical properties of self-dual bent functions",
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.",
keywords = "Boolean functions, Iterative construction, Metrical regularity, Self-dual bent",
author = "Aleksandr Kutsenko",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/s10623-019-00678-x",
language = "English",
volume = "88",
pages = "201--222",
journal = "Designs, Codes, and Cryptography",
issn = "0925-1022",
publisher = "Springer Netherlands",
number = "1",

}

RIS

TY - JOUR

T1 - Metrical properties of self-dual bent functions

AU - Kutsenko, Aleksandr

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Boolean functions

KW - Iterative construction

KW - Metrical regularity

KW - Self-dual bent

UR - http://www.scopus.com/inward/record.url?scp=85074030127&partnerID=8YFLogxK

U2 - 10.1007/s10623-019-00678-x

DO - 10.1007/s10623-019-00678-x

M3 - Article

AN - SCOPUS:85074030127

VL - 88

SP - 201

EP - 222

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

SN - 0925-1022

IS - 1

ER -

ID: 21997511