Nodal surfaces in P^3 and coding theory

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Kurz, Sascha:
Nodal surfaces in P^3 and coding theory.
Bayreuth , 2025 . - 11 S.

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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 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.