On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

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Title: On the construction of new bent functions from the max-weight and min-weight functions of old bent functions
Authors: Climent, Joan-Josep | García García, Francisco Jesús | Requena Arévalo, Verónica
Research Group/s: Grupo de Álgebra y Geometría (GAG)
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas | Universidad de Alicante. Departamento de Métodos Cuantitativos y Teoría Económica
Keywords: Boolean function | Linear function | Bent function | Support | Minterm | Max-weight function
Knowledge Area: Álgebra | Fundamentos del Análisis Económico
Issue Date: Dec-2015
Publisher: Springer Milan
Citation: SeMA Journal. 2015, 72(1): 13-36. doi:10.1007/s40324-015-0042-0
Abstract: Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.
URI: http://hdl.handle.net/10045/53310
ISSN: 2254-3902 (Print) | 2281-7875 (Online)
DOI: 10.1007/s40324-015-0042-0
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Sociedad Española de Matemática Aplicada 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/s40324-015-0042-0
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s40324-015-0042-0
Appears in Collections:INV - GAG - Artículos de Revistas

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