Ternary code construction of unimodular lattices and self-dual codes over ℤ6

Masaaki Harada, Masaaki Kitazume, Michio Ozeki

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9 Citations (Scopus)

Abstract

We revisit the construction method of even unimodular lattices using ternary self-dual codes given by the third author (M. Ozeki, in Théorie des nombres, J.-M. De Koninck and C. Levesque (Eds.) (Quebec, PQ, 1987), de Gruyter, Berlin, 1989, pp. 772-784), in order to apply the method to odd unimodular lattices and give some extremal (even and odd) unimodular lattices explicitly. In passing we correct an error on the condition for the minimum norm of the lattices of dimension a multiple of 12. As the results of our present research, extremal odd unimodular lattices in dimensions 44, 60 and 68 are constructed for the first time. It is shown that the unimodular lattices obtained by the method can be constructed from some self-dual ℤ6-codes. Then extremal self-dual ℤ6-codes of lengths 44, 48, 56, 60, 64 and 68 are constructed.

Original languageEnglish
Pages (from-to)209-223
Number of pages15
JournalJournal of Algebraic Combinatorics
Volume16
Issue number2
DOIs
Publication statusPublished - 2002 Sep

Keywords

  • Extremal self-dual ℤ-code
  • Extremal unimodular lattice
  • Ternary self-dual code

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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