Z6-Code Constructions of the Leech Lattice and the Niemeier Lattices

In this paper, we construct many new extremal Type II Z6-codes of length 24, and consequently we show that there is at least one extremal Type II Z6-code C of length 24 such that the binary and ternary reductions of C are B and T, respectively, for every binary Type II code B and every extremal ternary self-dual code T. These codes give more Z6-code constructions of the Leech lattice. It is also shown that every Niemeier lattice contains a (4 k2 + 2k + 6)-frame for every integer k.