Nodal surfaces in $\mathbb{P}^3$ and coding theory

Sascha Kurz

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arXiv · 2505.17531

Nodal surfaces in $\mathbb{P}^3$ and coding theory

Sascha Kurz

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Abstract

To each nodal hypersurface one can associate a binary linear code. Here we show that the binary linear code associated to sextics in $\mathbb{P}^3$ with the maximum number of $65$ nodes, as e.g. the Barth sextic, is unique. We also state possible candidates for codes that might be associated with a hypothetical septic attaining the currently best known upper bound for the maximum number of nodes.

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Sascha Kurz. 2025-05-23. Nodal surfaces in $\mathbb{P}^3$ and coding theory. https://arxiv.org/abs/2505.17531

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