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

Masaaki Harada, Masaaki Kitazume, Michio Ozeki

研究成果: Article査読

10 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)209-223
ページ数15
ジャーナルJournal of Algebraic Combinatorics
16
2
DOI
出版ステータスPublished - 2002 9月
外部発表はい

ASJC Scopus subject areas

  • 代数と数論
  • 離散数学と組合せ数学

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