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

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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.

Original languageEnglish
Pages (from-to)2345-2352
Number of pages8
JournalJournal of Algebra
Volume321
Issue number8
DOIs
Publication statusPublished - 2009 Apr 15

Keywords

  • Frame
  • Niemeier lattice
  • Self-dual code

ASJC Scopus subject areas

  • Algebra and Number Theory

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