Some observations on bent and planar functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911280290332672 |
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| author | Coulter, Robert S. Senger, Steven |
| author_facet | Coulter, Robert S. Senger, Steven |
| contents | We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a function, which applies to bent functions over fields of odd characteristic via their equivalence to perfect non-linear functions in that setting. We end by demonstrating, by entirely elementary means, that the distance between two distinct planar functions must be at least two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some observations on bent and planar functions Coulter, Robert S. Senger, Steven Combinatorics 11T06, 51E15, 06E30 We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a function, which applies to bent functions over fields of odd characteristic via their equivalence to perfect non-linear functions in that setting. We end by demonstrating, by entirely elementary means, that the distance between two distinct planar functions must be at least two. |
| title | Some observations on bent and planar functions |
| topic | Combinatorics 11T06, 51E15, 06E30 |
| url | https://arxiv.org/abs/2511.17815 |