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D. Jaffe and D. Ruberman proved in 1997 that a sextic hypersurface in$\mathbb{P}^3$ has at most 65 nodes (the bound is sharp by Barth'sconstruction).  Almost at the same time, J. Wahl proposed a much shorter proof of the sameresult, by proving that a linear code $V\subset \F^{66}$ with weights in$\{24,32,40\}$ has dimension $\dim(V)\leq12$.  He claimed that Jaffe-Ruberman's theorem follows as a corollary since thecode associated to a sextic with n nodes has dimension at least $n-53$ and anincorrect result stated by Casnati and Catanese asserted that the possiblecardinalities of an even set of nodes on a sextic were only 24, 32 and 40.  Recently Catanese and Tonoli showed that the possible cardinalities of aneven set of nodes on a sextic are exactly 24, 32, 40, 56. According to theabove cardinalities, the theorem of Jaffe and Ruberman reduces to thefollowing:  Let $V\subset \F^{66}$ be a code with weights in $\{24,32,40,56\}$. Then$\dim(V)\leq12$.  In this short note we give an elementary proof of this theorem using andintegrating Wahl's ideas.

On Wahl's proof of $\mu(6)=65$