On nonlinearity of Boolean functions generated by the generalized Dobbertin construction

I. A. Sutormin

Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia

Abstract: We propose a generalization of Dobbertin's 1995 construction for balanced highly nonlinear Boolean functions. The Walsh–Hadamard spectrum of the proposed functions is studied. An exact upper bound for the spectral radius (lower bound for nonlinearity) is achieved. We also introduce a method for constructing a balanced function of $2n$ variables and spectral radius $2^n + 2^k R$ using a balanced function of $n-k$ variables and spectral radius $R$. Bibliogr. 20.

Keywords: Boolean function, bent function, nonlinearity, balancedness, spectral radius.

UDC: 519.8+518.25

Received: 01.12.2020
Revised: 12.03.2021
Accepted: 15.03.2021

DOI: 10.33048/daio.2021.28.705

 English version: Journal of Applied and Industrial Mathematics, 2021, 15:3, 504–512