Corrections and additions to `` Pieces of $2^d$: existence and uniqueness for Barnes-Wall and Ypsilanti lattices. ''

Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices

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 lattices, which are families of indecomposable even unimodular lattices which resemble the Barnes-Wall latti…