On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916715300913152 |
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| author | Hou, Xiang-dong Zhao, Shujun |
| author_facet | Hou, Xiang-dong Zhao, Shujun |
| contents | A recent conjecture by C. Carlet on the sum-freedom of the binary multiplicative inverse function can be stated as follows: For each pair of positive integers $(n,k)$ with $3\le k\le n-3$, there is a $k$-dimensional $\Bbb F_2$-subspace $E$ of $\Bbb F_{2^n}$ such that $\sum_{0\ne\in E}1/u=0$. We confirm this conjecture when $n$ is not a prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function Hou, Xiang-dong Zhao, Shujun Number Theory 11G20, 11T06, 11T71, 94D10 A recent conjecture by C. Carlet on the sum-freedom of the binary multiplicative inverse function can be stated as follows: For each pair of positive integers $(n,k)$ with $3\le k\le n-3$, there is a $k$-dimensional $\Bbb F_2$-subspace $E$ of $\Bbb F_{2^n}$ such that $\sum_{0\ne\in E}1/u=0$. We confirm this conjecture when $n$ is not a prime. |
| title | On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function |
| topic | Number Theory 11G20, 11T06, 11T71, 94D10 |
| url | https://arxiv.org/abs/2504.21805 |