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- W2888339986 abstract "We prove the nonexistence of lattice tilings of $mathbb{Z}^n$ by Lee spheres of radius $2$ for all dimensions $ngeq 3$. This implies that the Golomb-Welch conjecture is true when the common radius of the Lee spheres equals $2$ and $2n^2+2n+1$ is a prime. As a direct consequence, we also answer an open question in the degree-diameter problem of graph theory: the order of any abelian Cayley graph of diameter $2$ and degree larger than $5$ cannot meet the abelian Cayley Moore bound." @default.
- W2888339986 created "2018-08-31" @default.
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- W2888339986 date "2018-08-26" @default.
- W2888339986 modified "2023-09-27" @default.
- W2888339986 title "There is no lattice tiling of $mathbb{Z}^n$ by Lee spheres of radius $2$ for $ngeq 3$" @default.
- W2888339986 hasPublicationYear "2018" @default.
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