Journal of Algebraic Combinatorics

, Volume 16, Issue 2, pp 209–223

Ternary Code Construction of Unimodular Lattices and Self-Dual Codes over ℤ6

  • Masaaki Harada
  • Masaaki Kitazume
  • Michio Ozeki
Article

DOI: 10.1023/A:1021185314365

Cite this article as:
Harada, M., Kitazume, M. & Ozeki, M. Journal of Algebraic Combinatorics (2002) 16: 209. doi:10.1023/A:1021185314365

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.

ternary self-dual codeextremal self-dual ℤ6-codeextremal unimodular lattice

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Masaaki Harada
    • 1
  • Masaaki Kitazume
    • 2
  • Michio Ozeki
    • 1
  1. 1.Department of Mathematical SciencesYamagata UniversityJapan
  2. 2.Department of Mathematics and InformaticsChiba UniversityJapan