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arXiv · 2504.21805

On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function

Xiang-dong Hou·Shujun Zhao
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Abstract

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.

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Xiang-dong Hou, Shujun Zhao. 2025-04-30. On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function. https://arxiv.org/abs/2504.21805

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