Double Circulant Codes over $$\mathbb{Z}_4 $$ and Even Unimodular Lattices

AbstractWith the help of some new results about weight enumerators of self-dual codes over $$\mathbb{Z}_4 $$ we investigate a class of double circulant codes over $$\mathbb{Z}_4 $$ , one of which leads to an extremal even unimodular 40–dimensional lattice. It is conjectured that there should be “Nine more constructions of the Leech lattice”

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