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We revisit the construction method of even unimodular lattices using ternary self-dual codes given by the third author (M. Ozeki, in , 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 ℤ-codes. Then extremal self-dual ℤ-codes of lengths 44, 48, 56, 60, 64 and 68 are constructed.

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