Nodal surfaces in $\mathbb{P}^3$ and coding theory
Combinatorics
2025-05-26 v1 Information Theory
Algebraic Geometry
math.IT
Abstract
To each nodal hypersurface one can associate a binary linear code. Here we show that the binary linear code associated to sextics in with the maximum number of 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.
Cite
@article{arxiv.2505.17531,
title = {Nodal surfaces in $\mathbb{P}^3$ and coding theory},
author = {Sascha Kurz},
journal= {arXiv preprint arXiv:2505.17531},
year = {2025}
}
Comments
11 pages