We show that the lattice Hadwiger number of superballs is exponential in the
dimension. The same is true for some more general convex bodies.Comment: 7 pages, the construction is correcte

Vlăduţ, Serge

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arXiv

We show that the lattice Hadwiger number of superballs is exponential in the dimension. The same is true for some more general convex bodies.Unfortunately, the main result of the paper should be considered as not proven. Namely, the construction D applied to a code $C_0$ with many light vectors gives a lattice $L$ but there is no proof that the kissing number of $L$ is exponential. The initial impression that this lattice retains all the short vectors (light vectors considered as 0-1 vectors) from $C_0$ is definitely fals

On the lattice Hadwiger number of superballs and some other bodies

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