TY - JOUR

T1 - Metrical properties of the set of bent functions in view of duality

AU - Kutsenko, A. V.

AU - Tokareva, N. N.

N1 - Publisher Copyright: © 2020 Tomsk State University. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/9

Y1 - 2020/9

N2 - In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n+2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n ≥ 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered.

AB - In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n+2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n ≥ 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered.

KW - Automorphism group

KW - Boolean bent function

KW - Hamming distance

KW - Iterative construction

KW - Metrical regularity

KW - Self-dual bent function

KW - metrical regularity

KW - iterative construction

KW - automorphism group

KW - self-dual bent function

KW - AUTOMORPHISMS

UR - http://www.scopus.com/inward/record.url?scp=85095876417&partnerID=8YFLogxK

U2 - 10.17223/20710410/49/2

DO - 10.17223/20710410/49/2

M3 - Review article

AN - SCOPUS:85095876417

SP - 18

EP - 34

JO - Прикладная дискретная математика

JF - Прикладная дискретная математика

SN - 2071-0410

IS - 49

ER -