Z6-code constructions of the Leech lattice and the Niemeier lattices

Authors:
Masaaki Harada;Masaaki Kitazume
Affiliations:
Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan;Department of Mathematics and Informatics, Chiba University, Chiba 263-8522, Japan
Venue:
European Journal of Combinatorics
Year:
2002

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Abstract

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 (4k2 + 2k + 6)-frame for every integer k.