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Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function. / Куценко, Александр Владимирович.

в: Прикладная дискретная математика, № 69, 2, 2025, стр. 18-36.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Куценко, АВ 2025, 'Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function', Прикладная дискретная математика, № 69, 2, стр. 18-36. https://doi.org/10.17223/20710410/69/2

APA

Куценко, А. В. (2025). Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function. Прикладная дискретная математика, (69), 18-36. [2]. https://doi.org/10.17223/20710410/69/2

Vancouver

Куценко АВ. Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function. Прикладная дискретная математика. 2025;(69):18-36. 2. doi: 10.17223/20710410/69/2

Author

Куценко, Александр Владимирович. / Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function. в: Прикладная дискретная математика. 2025 ; № 69. стр. 18-36.

BibTeX

@article{744839ab6c0341879aafac92771827eb,
title = "Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function",
abstract = "A generalized Boolean function with flat Walsh - Hadamard spectrum is called generalized bent (gbent) function. Gbent function that coincides with its dual bent function is called self-dual. In this paper, we study isometric mappings of the set of all generalized Boolean functions into itself that preserve self-duality. A new mapping that preserves the self-duality of a gbent function is proposed. We introduce the concept of the action of an unitary operator on the set of generalized Boolean functions in n variables, represented by their characteristic vectors. Within the considered class of unitary operators, all mappings that preserve self-duality are described. A generalized form of isometric mapping corresponding to the complex conjugation of the characteristic vector is investigated.",
keywords = "ОБОБЩЁННАЯ БЕНТ-ФУНКЦИЯ, САМОДУАЛЪНАЯ БЕНТ-ФУНКЦИЯ, ИЗОМЕТРИЧНОЕ ОТОБРАЖЕНИЕ, GENERALIZED BOOLEAN FUNCTION, SELF-DUAL BENT FINCTION, ISOMETRIC MAPPING",
author = "Куценко, {Александр Владимирович}",
note = "Куценко, А. В. Описание некоторых классов изометричных отображений, сохраняющих самодуальность обобщённой бент-функции / А. В. Куценко // Прикладная дискретная математика. – 2025. – № 69. – С. 18-36. – DOI 10.17223/20710410/69/2. – EDN NDCPTF. Работа выполнена при поддержке Математического центра в Академгородке, соглашение с Министерством науки и высшего образования РФ № 075-15-2025-349.",
year = "2025",
doi = "10.17223/20710410/69/2",
language = "English",
pages = "18--36",
journal = "Прикладная дискретная математика",
issn = "2071-0410",
publisher = "Издательство: Национальный исследовательский Томский государственный университет",
number = "69",

}

RIS

TY - JOUR

T1 - Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function

AU - Куценко, Александр Владимирович

N1 - Куценко, А. В. Описание некоторых классов изометричных отображений, сохраняющих самодуальность обобщённой бент-функции / А. В. Куценко // Прикладная дискретная математика. – 2025. – № 69. – С. 18-36. – DOI 10.17223/20710410/69/2. – EDN NDCPTF. Работа выполнена при поддержке Математического центра в Академгородке, соглашение с Министерством науки и высшего образования РФ № 075-15-2025-349.

PY - 2025

Y1 - 2025

N2 - A generalized Boolean function with flat Walsh - Hadamard spectrum is called generalized bent (gbent) function. Gbent function that coincides with its dual bent function is called self-dual. In this paper, we study isometric mappings of the set of all generalized Boolean functions into itself that preserve self-duality. A new mapping that preserves the self-duality of a gbent function is proposed. We introduce the concept of the action of an unitary operator on the set of generalized Boolean functions in n variables, represented by their characteristic vectors. Within the considered class of unitary operators, all mappings that preserve self-duality are described. A generalized form of isometric mapping corresponding to the complex conjugation of the characteristic vector is investigated.

AB - A generalized Boolean function with flat Walsh - Hadamard spectrum is called generalized bent (gbent) function. Gbent function that coincides with its dual bent function is called self-dual. In this paper, we study isometric mappings of the set of all generalized Boolean functions into itself that preserve self-duality. A new mapping that preserves the self-duality of a gbent function is proposed. We introduce the concept of the action of an unitary operator on the set of generalized Boolean functions in n variables, represented by their characteristic vectors. Within the considered class of unitary operators, all mappings that preserve self-duality are described. A generalized form of isometric mapping corresponding to the complex conjugation of the characteristic vector is investigated.

KW - ОБОБЩЁННАЯ БЕНТ-ФУНКЦИЯ

KW - САМОДУАЛЪНАЯ БЕНТ-ФУНКЦИЯ

KW - ИЗОМЕТРИЧНОЕ ОТОБРАЖЕНИЕ

KW - GENERALIZED BOOLEAN FUNCTION

KW - SELF-DUAL BENT FINCTION

KW - ISOMETRIC MAPPING

UR - https://www.scopus.com/pages/publications/105024448278

UR - https://elibrary.ru/item.asp?id=83025877

UR - https://www.mendeley.com/catalogue/92135981-d73e-301e-9931-33f5f03a4bc4/

U2 - 10.17223/20710410/69/2

DO - 10.17223/20710410/69/2

M3 - Article

SP - 18

EP - 36

JO - Прикладная дискретная математика

JF - Прикладная дискретная математика

SN - 2071-0410

IS - 69

M1 - 2

ER -

ID: 72669982