On two open problems on the normality of bent functions

Alexandr Polujan; Luca Mariot; Stjepan Picek

doi:10.1016/j.dam.2024.08.023

On two open problems on the normality of bent functions

Alexandr Polujan^*
, Luca Mariot
, Stjepan Picek

^*Corresponding author for this work

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

3 Citations (Scopus)

172 Downloads (Pure)

Abstract

Non-normal Boolean bent functions are one of the least understood classes of bent functions, and only a few difficult-to-find examples of such functions are known. In this paper, we consider the following two open problems on the normality of bent functions: 1. Do non-normal bent functions in 8 variables and degree 4 exist? 2. Do non-normal bent functions in the PS⁻∖PS_ap class exist? We solve both of these problems by finding among the known PS bent functions in n=8 variables a non-normal bent function in the PS⁻∖PS_ap class.

Original language	English
Pages (from-to)	115-118
Number of pages	4
Journal	Discrete applied mathematics
Volume	360
DOIs	https://doi.org/10.1016/j.dam.2024.08.023
Publication status	Published - 15 Jan 2025

Keywords

Boolean bent function
Normality
Partial spread class

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10.1016/j.dam.2024.08.023Licence: CC BY

1-s2.0-S0166218X24003901-mainFinal published version, 390 KBLicence: CC BY

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title = "On two open problems on the normality of bent functions",

abstract = "Non-normal Boolean bent functions are one of the least understood classes of bent functions, and only a few difficult-to-find examples of such functions are known. In this paper, we consider the following two open problems on the normality of bent functions: 1. Do non-normal bent functions in 8 variables and degree 4 exist? 2. Do non-normal bent functions in the PS−∖PSap class exist? We solve both of these problems by finding among the known PS bent functions in n=8 variables a non-normal bent function in the PS−∖PSap class.",

keywords = "Boolean bent function, Normality, Partial spread class",

author = "Alexandr Polujan and Luca Mariot and Stjepan Picek",

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T1 - On two open problems on the normality of bent functions

AU - Polujan, Alexandr

AU - Mariot, Luca

AU - Picek, Stjepan

PY - 2025/1/15

Y1 - 2025/1/15

N2 - Non-normal Boolean bent functions are one of the least understood classes of bent functions, and only a few difficult-to-find examples of such functions are known. In this paper, we consider the following two open problems on the normality of bent functions: 1. Do non-normal bent functions in 8 variables and degree 4 exist? 2. Do non-normal bent functions in the PS−∖PSap class exist? We solve both of these problems by finding among the known PS bent functions in n=8 variables a non-normal bent function in the PS−∖PSap class.

AB - Non-normal Boolean bent functions are one of the least understood classes of bent functions, and only a few difficult-to-find examples of such functions are known. In this paper, we consider the following two open problems on the normality of bent functions: 1. Do non-normal bent functions in 8 variables and degree 4 exist? 2. Do non-normal bent functions in the PS−∖PSap class exist? We solve both of these problems by finding among the known PS bent functions in n=8 variables a non-normal bent function in the PS−∖PSap class.

KW - Boolean bent function

KW - Normality

KW - Partial spread class

UR - https://www.scopus.com/pages/publications/85203183941

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DO - 10.1016/j.dam.2024.08.023

M3 - Article

AN - SCOPUS:85203183941

SN - 0166-218X

VL - 360

SP - 115

EP - 118

JO - Discrete applied mathematics

JF - Discrete applied mathematics

ER -

On two open problems on the normality of bent functions

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