On the existence of frames of the Niemeier lattices and self-dual codes over \(\mathbb F_p\)
The Niemeier lattices are the 24 non-isomorphic 24-dimensional even unimodular lattices. Montague has shown that every Niemeier lattice can be constructed as an even unimodular neighbor of an odd unimodular lattice obtained from a self-dual code over \(F_3\) via construction A. The author proves that every Niemeier lattice can be constructed as an even unimodular neighbor of an odd unimodular lattice obtained from a self-dual code over \(F_p\) for each prime \(p\) with \(5 \leq p \leq 23\). A consequence is that every Niemeier lattice contains a \(2k\)-frame for \(k= 2, 3,\dots, 28\).
scientific article; zbMATH DE number 5565635