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

✍ Scribed by Masaaki Harada; Masaaki Kitazume

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 95 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0557

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✦ Synopsis

In this paper, we construct many new extremal Type II Z 6 -codes of length 24, and consequently we show that there is at least one extremal Type II Z 6 -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 Z 6 -code constructions of the Leech lattice. It is also shown that every Niemeier lattice contains a (4k 2 + 2k + 6)-frame for every integer k.

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