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

2025/04/30 by Hou, Xiang-dong, Zhao, Shujun · 1 citation
#11G20 #11T06 #11T71 #94D10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.21805

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≤ k≤ n-3, there is a k-dimensional \Bbb F₂-subspace E of \Bbb F_2ⁿ such that ∑_{0≠∈ E}1/u=0. We confirm this conjecture when n is not a prime.

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• Applying hypersurface bounds to a conjecture by Carlet

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