On the max min of the algebraic degree and the nonlinearity of a Boolean function on an affine subspace
| Autor: | Haugland, Jan Kristian |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pages. Added information on how the examples in Section 3 were found. Those examples given in the first version have been replaced by equivalent functions with fewer terms in the ANF, kindly communicated by Langevin |
| Databáze: | arXiv |
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