An estimation of the nonlinearity of balanced boolean functions generated by generalized dob-bertin's construction | Applied Discrete Mathematics. Supplement. 2020. № 13. DOI: 10.17223/2226308X/13/9

An estimation of the nonlinearity of balanced boolean functions generated by generalized dob-bertin's construction

A generalization of the Dobbertin's construction for highly nonlinear balanced Boolean functions is proposed. The Walsh - Hadamard spectrum is studied and estimates of the spectral radius of the proposed functions are obtained. An exact upper bound for the spectral radius (lower bound for nonlinearity) is proved, and a method for constructing a balanced function в in 2n variables using a balanced в in n - k variables with spectral radius R© = 2ⁿ + 2^kRe is proposed. Here, R© and Re are the spectral radii of в and в respectively.

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Keywords

булевы функции, бент-функции, сбалансированность, нелинейность, спектральный радиус, boolean functions, bent functions, balancedness, nonlinearity, spectral radius

Authors

Name	Organization	E-mail
Sutormin I.A.	S. L. Sobolev Institute of Mathematics SB RAS; Novosibirsk State University	ivan.sutormin@gmail.com

Всего: 1

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