Geodesic
Ternary code construction of unimodular lattices and self-dual codes over $\Bbb Z_6$
Journal of Algebraic Combinatorics, Tome 16 (2002) no. 2, pp. 209-223.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $Zopf _{6}$-codes. Then extremal self-dual $Zopf _{6}$-codes of lengths 44, 48, 56, 60, 64 and 68 are constructed.
Keywords: ternary self-dual code, extremal self-dual $Zopf _{6}$-code, extremal unimodular lattice 
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     author = {Harada, Masaaki and Kitazume, Masaaki and Ozeki, Michio},
     title = {Ternary code construction of unimodular lattices and self-dual codes over $\Bbb Z_6$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {209--223},
     publisher = {mathdoc},
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     number = {2},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2002__16_2_a0/}
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Harada, Masaaki; Kitazume, Masaaki; Ozeki, Michio. Ternary code construction of unimodular lattices and self-dual codes over $\Bbb Z_6$. Journal of Algebraic Combinatorics, Tome 16 (2002) no. 2, pp. 209-223. http://geodesic.mathdoc.fr/item/JAC_2002__16_2_a0/