Quadratic rotation symmetric Boolean functions

Alexandru Chirvasitu; Thomas W. Cusick

doi:10.1016/j.dam.2023.10.010

Quadratic rotation symmetric Boolean functions

Mathematics

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

3 Scopus citations

Abstract

Let (0,a₁,…,a_d−1)_n denote the function f_n(x₀,x₁,…,x_n−1) of degree d in n variables generated by the monomial x₀x_a₁⋯x_{a_d−1} and having the property that f_n is invariant under cyclic permutations of the variables. Such a function f_n is called monomial rotation symmetric (MRS). Much of this paper extends the work on quadratic MRS functions in a 2020 paper of the authors to the case of binomial RS functions, that is sums of two quadratic MRS functions. There are also some results for the sum of any number of quadratic MRS functions.

Original language	English
Pages (from-to)	91-105
Number of pages	15
Journal	Discrete Applied Mathematics
Volume	343
DOIs	https://doi.org/10.1016/j.dam.2023.10.010
State	Published - Jan 30 2024

Keywords

Balanced function
Boolean function
Hamming weight
Rotation symmetric

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10.1016/j.dam.2023.10.010

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title = "Quadratic rotation symmetric Boolean functions",

abstract = "Let (0,a1,…,ad−1)n denote the function fn(x0,x1,…,xn−1) of degree d in n variables generated by the monomial x0xa1⋯xad−1 and having the property that fn is invariant under cyclic permutations of the variables. Such a function fn is called monomial rotation symmetric (MRS). Much of this paper extends the work on quadratic MRS functions in a 2020 paper of the authors to the case of binomial RS functions, that is sums of two quadratic MRS functions. There are also some results for the sum of any number of quadratic MRS functions.",

keywords = "Balanced function, Boolean function, Hamming weight, Rotation symmetric",

author = "Alexandru Chirvasitu and Cusick, \{Thomas W.\}",

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year = "2024",

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doi = "10.1016/j.dam.2023.10.010",

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T1 - Quadratic rotation symmetric Boolean functions

AU - Chirvasitu, Alexandru

AU - Cusick, Thomas W.

PY - 2024/1/30

Y1 - 2024/1/30

N2 - Let (0,a1,…,ad−1)n denote the function fn(x0,x1,…,xn−1) of degree d in n variables generated by the monomial x0xa1⋯xad−1 and having the property that fn is invariant under cyclic permutations of the variables. Such a function fn is called monomial rotation symmetric (MRS). Much of this paper extends the work on quadratic MRS functions in a 2020 paper of the authors to the case of binomial RS functions, that is sums of two quadratic MRS functions. There are also some results for the sum of any number of quadratic MRS functions.

AB - Let (0,a1,…,ad−1)n denote the function fn(x0,x1,…,xn−1) of degree d in n variables generated by the monomial x0xa1⋯xad−1 and having the property that fn is invariant under cyclic permutations of the variables. Such a function fn is called monomial rotation symmetric (MRS). Much of this paper extends the work on quadratic MRS functions in a 2020 paper of the authors to the case of binomial RS functions, that is sums of two quadratic MRS functions. There are also some results for the sum of any number of quadratic MRS functions.

KW - Balanced function

KW - Boolean function

KW - Hamming weight

KW - Rotation symmetric

UR - https://www.scopus.com/pages/publications/85174606392

U2 - 10.1016/j.dam.2023.10.010

DO - 10.1016/j.dam.2023.10.010

M3 - Article

AN - SCOPUS:85174606392

SN - 0166-218X

VL - 343

SP - 91

EP - 105

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Quadratic rotation symmetric Boolean functions

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Keywords

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