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A lower bound on the size of the largest metrically regular subset of the Boolean cube. / Oblaukhov, Alexey.

In: Cryptography and Communications, Vol. 11, No. 4, 15.07.2019, p. 777-791.

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

Harvard

Oblaukhov, A 2019, 'A lower bound on the size of the largest metrically regular subset of the Boolean cube', Cryptography and Communications, vol. 11, no. 4, pp. 777-791. https://doi.org/10.1007/s12095-018-0326-1

APA

Oblaukhov, A. (2019). A lower bound on the size of the largest metrically regular subset of the Boolean cube. Cryptography and Communications, 11(4), 777-791. https://doi.org/10.1007/s12095-018-0326-1

Vancouver

Oblaukhov A. A lower bound on the size of the largest metrically regular subset of the Boolean cube. Cryptography and Communications. 2019 Jul 15;11(4):777-791. doi: 10.1007/s12095-018-0326-1

Author

Oblaukhov, Alexey. / A lower bound on the size of the largest metrically regular subset of the Boolean cube. In: Cryptography and Communications. 2019 ; Vol. 11, No. 4. pp. 777-791.

BibTeX

@article{1ca2a4cfb2df45dcb185df910edf872d,
title = "A lower bound on the size of the largest metrically regular subset of the Boolean cube",
abstract = "Let A be an arbitrary subset of the Boolean cube, and {\^A} be the set of all vectors of the Boolean cube, which are at the maximal possible distance from the set A. If the set of all vectors at the maximal distance from {\^A} coincides with A, then the set A is called a metrically regular set. The problem of investigating metrically regular sets appears when studying bent functions, which have important applications in cryptography and coding theory. In this work a special subclass of strongly metrically regular subsets of the Boolean cube is studied. An iterative construction of strongly metrically regular sets is obtained. The formula for the number of sets which can be obtained via this construction is derived. Constructions for two families of large metrically regular sets are presented. Exact sizes of sets from these families are calculated. These sizes give us the best lower bound on sizes of largest metrically regular subsets of the Boolean cube.",
keywords = "Bent function, Boolean cube, Metric complement, Metrically regular set, Strongly metrically regular set",
author = "Alexey Oblaukhov",
note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2019",
month = jul,
day = "15",
doi = "10.1007/s12095-018-0326-1",
language = "English",
volume = "11",
pages = "777--791",
journal = "Cryptography and Communications",
issn = "1936-2447",
publisher = "Springer Publishing Company",
number = "4",

}

RIS

TY - JOUR

T1 - A lower bound on the size of the largest metrically regular subset of the Boolean cube

AU - Oblaukhov, Alexey

N1 - Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019/7/15

Y1 - 2019/7/15

N2 - Let A be an arbitrary subset of the Boolean cube, and  be the set of all vectors of the Boolean cube, which are at the maximal possible distance from the set A. If the set of all vectors at the maximal distance from  coincides with A, then the set A is called a metrically regular set. The problem of investigating metrically regular sets appears when studying bent functions, which have important applications in cryptography and coding theory. In this work a special subclass of strongly metrically regular subsets of the Boolean cube is studied. An iterative construction of strongly metrically regular sets is obtained. The formula for the number of sets which can be obtained via this construction is derived. Constructions for two families of large metrically regular sets are presented. Exact sizes of sets from these families are calculated. These sizes give us the best lower bound on sizes of largest metrically regular subsets of the Boolean cube.

AB - Let A be an arbitrary subset of the Boolean cube, and  be the set of all vectors of the Boolean cube, which are at the maximal possible distance from the set A. If the set of all vectors at the maximal distance from  coincides with A, then the set A is called a metrically regular set. The problem of investigating metrically regular sets appears when studying bent functions, which have important applications in cryptography and coding theory. In this work a special subclass of strongly metrically regular subsets of the Boolean cube is studied. An iterative construction of strongly metrically regular sets is obtained. The formula for the number of sets which can be obtained via this construction is derived. Constructions for two families of large metrically regular sets are presented. Exact sizes of sets from these families are calculated. These sizes give us the best lower bound on sizes of largest metrically regular subsets of the Boolean cube.

KW - Bent function

KW - Boolean cube

KW - Metric complement

KW - Metrically regular set

KW - Strongly metrically regular set

UR - http://www.scopus.com/inward/record.url?scp=85068131626&partnerID=8YFLogxK

U2 - 10.1007/s12095-018-0326-1

DO - 10.1007/s12095-018-0326-1

M3 - Article

AN - SCOPUS:85068131626

VL - 11

SP - 777

EP - 791

JO - Cryptography and Communications

JF - Cryptography and Communications

SN - 1936-2447

IS - 4

ER -

ID: 20710677