On the normality of Boolean quartics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914879424692224 |
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| author | Gillot, Valérie Langevin, Philippe Polujan, Alexandr |
| author_facet | Gillot, Valérie Langevin, Philippe Polujan, Alexandr |
| contents | In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we present numerical approaches based on the classification of Boolean spaces to explore in detail the normality of bent functions of 8 variables and we complete S. Dubuc s results for dimensions less or equal to 7. Based on our investigations, we show that all bent functions in 8 variables are normal or weakly normal. Finally, we conjecture that more generally all Boolean functions of degree at most 4 in 8 variables are normal or weakly normal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_14038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the normality of Boolean quartics Gillot, Valérie Langevin, Philippe Polujan, Alexandr Discrete Mathematics 06E30 In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we present numerical approaches based on the classification of Boolean spaces to explore in detail the normality of bent functions of 8 variables and we complete S. Dubuc s results for dimensions less or equal to 7. Based on our investigations, we show that all bent functions in 8 variables are normal or weakly normal. Finally, we conjecture that more generally all Boolean functions of degree at most 4 in 8 variables are normal or weakly normal. |
| title | On the normality of Boolean quartics |
| topic | Discrete Mathematics 06E30 |
| url | https://arxiv.org/abs/2407.14038 |