Quadratic bent functions and their duals

Kanat Abdukhalikov; Rongquan Feng; Duy Ho

doi:10.1007/s00200-022-00564-5

Quadratic bent functions and their duals

Kanat Abdukhalikov
, Rongquan Feng
, Duy Ho

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using the zeros of the polynomial X^q+1+X+a which have been studied recently in the literature, we provide some examples of binomial quadratic bent functions on Fq₄ and Fq₆, where q is a power of 2.

Original language	English
Pages (from-to)	507-523
Number of pages	17
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	35
Issue number	4
DOIs	https://doi.org/10.1007/s00200-022-00564-5
Publication status	Published - Jul 2024

Keywords

51E15
51E20
94A60
Bent functions
Duals of bent functions
Quadratic bent functions

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1007/s00200-022-00564-5

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author = "Kanat Abdukhalikov and Rongquan Feng and Duy Ho",

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AU - Ho, Duy

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022.

PY - 2024/7

Y1 - 2024/7

N2 - We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using the zeros of the polynomial Xq+1+X+a which have been studied recently in the literature, we provide some examples of binomial quadratic bent functions on Fq4 and Fq6, where q is a power of 2.

AB - We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using the zeros of the polynomial Xq+1+X+a which have been studied recently in the literature, we provide some examples of binomial quadratic bent functions on Fq4 and Fq6, where q is a power of 2.

KW - 51E15

KW - 51E20

KW - 94A60

KW - Bent functions

KW - Duals of bent functions

KW - Quadratic bent functions

UR - https://www.scopus.com/pages/publications/85131835180

UR - https://www.scopus.com/pages/publications/85131835180#tab=citedBy

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JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

IS - 4

ER -

Quadratic bent functions and their duals

Abstract

Keywords

ASJC Scopus subject areas

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