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Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices
[article]
2004
arXiv
pre-print
We give a new existence proof for the rank 2^d even lattices usually called the Barnes-Wall lattices, and establish new results on uniqueness, structure and transitivity of the automorphism group on certain kinds of sublattices. Our proofs are relatively free of calculations, matrix work and counting, due to the uniqueness viewpoint. We deduce the labeling of coordinates on which earlier constructions depend. Extending these ideas, we construct in dimensions 2^d, for d>>0, the Ypsilanti
arXiv:math/0403480v1
fatcat:z4xqji3fcvhl3jicekt4i4y2qm