On the existence of frames of the Niemeier lattices and self-dual codes over Fp

Masaaki Harada

doi:10.1016/j.jalgebra.2009.02.001

On the existence of frames of the Niemeier lattices and self-dual codes over F_p

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

Abstract

Motivated by the work of Montague in 1994, we demonstrate that every Niemeier lattice can be constructed as an even unimodular neighbor of the odd unimodular lattice obtained from some self-dual code over F_p by Construction A for each prime number p with 5 ≤ p ≤ 23. This implies that every Niemeier lattice contains a 2k-frame for k = 2, 3, ..., 28.

Original language	English
Pages (from-to)	2345-2352
Number of pages	8
Journal	Journal of Algebra
Volume	321
Issue number	8
DOIs	https://doi.org/10.1016/j.jalgebra.2009.02.001
Publication status	Published - 2009 Apr 15
Externally published	Yes

Keywords

Frame
Niemeier lattice
Self-dual code

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2009.02.001

Cite this

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abstract = "Motivated by the work of Montague in 1994, we demonstrate that every Niemeier lattice can be constructed as an even unimodular neighbor of the odd unimodular lattice obtained from some self-dual code over Fp by Construction A for each prime number p with 5 ≤ p ≤ 23. This implies that every Niemeier lattice contains a 2k-frame for k = 2, 3, ..., 28.",

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AB - Motivated by the work of Montague in 1994, we demonstrate that every Niemeier lattice can be constructed as an even unimodular neighbor of the odd unimodular lattice obtained from some self-dual code over Fp by Construction A for each prime number p with 5 ≤ p ≤ 23. This implies that every Niemeier lattice contains a 2k-frame for k = 2, 3, ..., 28.

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KW - Self-dual code

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