The binary linear code associated to any sextic surface in P^3 with 65 nodes is unique: it is the [65,12,{24,32,40}] code of the Barth sextic.
Minimal even sets of nodes
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We extend some results on even sets of nodes which have been proved for surfaces up to degree 6 to surfaces up to degree 10. In particular, we give a formula for the minimal cardinality of a nonempty even set of nodes.
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math.CO 1years
2025 1verdicts
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Nodal surfaces in $\mathbb{P}^3$ and coding theory
The binary linear code associated to any sextic surface in P^3 with 65 nodes is unique: it is the [65,12,{24,32,40}] code of the Barth sextic.