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arXiv · 2408.01477

On the max min of the algebraic degree and the nonlinearity of a Boolean function on an affine subspace

Jan Kristian Haugland
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Abstract

We investigate the max min of the algebraic degree and the nonlinearity of a Boolean function in $n$ variables when restricted to a $k$-dimensional affine subspace of $\mathbb{F}_2^n$. Previous authors have focused on the cases when the max min of the algebraic degree is 0 or 1. Upper bounds, lower bounds and a conjecture on the exact value in special cases are presented.

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Jan Kristian Haugland. 2024-09-05. On the max min of the algebraic degree and the nonlinearity of a Boolean function on an affine subspace. https://doi.org/10.1016/j.dam.2025.02.022

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