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.
Sur le nombre maximum de points doubles d’une surface dans P ^3 ( (5)= 31 )
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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.