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

Authors:
Masaaki Harada; Masaaki Kitazume; Michio Ozeki
Affiliations:
Department of Mathematical Sciences, Yamagata University, Yamagata 990–8560, Japan;Department of Mathematics and Informatics, Chiba University, Chiba 263–8522, Japan;Department of Mathematical Sciences, Yamagata University, Yamagata 990–8560, Japan
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2002

Citing 4
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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 \Bbb Z6-codes. Then extremal self-dual \Bbb Z6-codes of lengths 44, 48, 56, 60, 64 and 68 are constructed.