Homogeneous bent functions of degree n in 2n variables do not exist for n > 3

Tianbing Xia; Jennifer Seberry; Josef Pieprzyk; Chris Charnes

doi:10.1016/j.dam.2004.02.006

Homogeneous bent functions of degree n in 2n variables do not exist for n > 3

Tianbing Xia^*, Jennifer Seberry, Josef Pieprzyk, Chris Charnes

^*Corresponding author for this work

School of Computing

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

24 Citations (Scopus)

Abstract

The nonexistance of homogeneous bent functions of degree n in 2n variables for n > 3 was analyzed. For the analysis, a certain decomposition of a Menon difference set, which corrosponds to bent function was used. The results show that there is no homogeneous bent function of degree 4 in 8 Boolean variables. However, it was suggested that there are few execeptions such as 3-homogeneous Boolean functions of 6 variables, and the 2-homogeneous Boolean functions of 4 variables.

Original language	English
Pages (from-to)	127-132
Number of pages	6
Journal	Discrete Applied Mathematics
Volume	142
Issue number	1-3 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.dam.2004.02.006
Publication status	Published - 15 Aug 2004

Keywords

Bent
Difference sets
Homogeneous

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abstract = "The nonexistance of homogeneous bent functions of degree n in 2n variables for n > 3 was analyzed. For the analysis, a certain decomposition of a Menon difference set, which corrosponds to bent function was used. The results show that there is no homogeneous bent function of degree 4 in 8 Boolean variables. However, it was suggested that there are few execeptions such as 3-homogeneous Boolean functions of 6 variables, and the 2-homogeneous Boolean functions of 4 variables.",

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AU - Xia, Tianbing

AU - Seberry, Jennifer

AU - Pieprzyk, Josef

AU - Charnes, Chris

PY - 2004/8/15

Y1 - 2004/8/15

N2 - The nonexistance of homogeneous bent functions of degree n in 2n variables for n > 3 was analyzed. For the analysis, a certain decomposition of a Menon difference set, which corrosponds to bent function was used. The results show that there is no homogeneous bent function of degree 4 in 8 Boolean variables. However, it was suggested that there are few execeptions such as 3-homogeneous Boolean functions of 6 variables, and the 2-homogeneous Boolean functions of 4 variables.

AB - The nonexistance of homogeneous bent functions of degree n in 2n variables for n > 3 was analyzed. For the analysis, a certain decomposition of a Menon difference set, which corrosponds to bent function was used. The results show that there is no homogeneous bent function of degree 4 in 8 Boolean variables. However, it was suggested that there are few execeptions such as 3-homogeneous Boolean functions of 6 variables, and the 2-homogeneous Boolean functions of 4 variables.

KW - Bent

KW - Difference sets

KW - Homogeneous

UR - https://www.scopus.com/pages/publications/3142537092

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DO - 10.1016/j.dam.2004.02.006

M3 - Article

AN - SCOPUS:3142537092

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SP - 127

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 1-3 SPEC. ISS.

ER -

Homogeneous bent functions of degree n in 2n variables do not exist for n > 3

Abstract

Keywords

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