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

Masaaki Harada; Masaaki Kitazume

doi:10.1006/eujc.2002.0557

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

Masaaki Harada, Masaaki Kitazume

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	573-581
Number of pages	9
Journal	European Journal of Combinatorics
Volume	23
Issue number	5
DOIs	https://doi.org/10.1006/eujc.2002.0557
Publication status	Published - 2002 Jul

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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title = "ℤ6-code constructions of the Leech lattice and the Niemeier lattices",

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.",

author = "Masaaki Harada and Masaaki Kitazume",

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AB - 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.

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