Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)
The Leech lattice has previously been constructed from a self-dual code over the ring \(\mathbb{Z}_4\). There are 22 other even unimodular lattices in dimension 24. This paper shows that all of these lattices can be constructed from self-dual codes over \(\mathbb{Z}_4\). Generator matrices and symmetric weight enumerators are given for these codes. It is also shown that all extremal unimodular lattices can be constructed from self-dual codes over \(\mathbb{Z}_4\).
scientific article; zbMATH DE number 1334673