Geodesic
On nonlinearity of Boolean functions generated by the generalized Dobbertin construction
Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 3, pp. 49-64.

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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. 
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I. A. Sutormin. On nonlinearity of Boolean functions generated by the generalized Dobbertin construction. Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 3, pp. 49-64. http://geodesic.mathdoc.fr/item/DA_2021_28_3_a2/

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