A lower bound on the number of bent squares
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916938716807168 |
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| author | Haugland, Jan Kristian |
| author_facet | Haugland, Jan Kristian |
| contents | Bent functions are Boolean functions that are maximally nonlinear. They can be represented as bent squares, i.e., square matrices for which each row and each column is the Walsh spectrum of a Boolean function. Using this representation, it is shown in this note that the number of bent functions in $n$ variables is at least $2^{n \cdot 2^{\frac{n}{2}} \left(1 + O\left(\frac{1}{n}\right)\right)}$ for even integers $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A lower bound on the number of bent squares Haugland, Jan Kristian Combinatorics 06E30 Bent functions are Boolean functions that are maximally nonlinear. They can be represented as bent squares, i.e., square matrices for which each row and each column is the Walsh spectrum of a Boolean function. Using this representation, it is shown in this note that the number of bent functions in $n$ variables is at least $2^{n \cdot 2^{\frac{n}{2}} \left(1 + O\left(\frac{1}{n}\right)\right)}$ for even integers $n$. |
| title | A lower bound on the number of bent squares |
| topic | Combinatorics 06E30 |
| url | https://arxiv.org/abs/2508.14605 |