Certain lattice neighboring from Barnes-Wall lattice and some laminated lattices

Details Certain lattice neighboring from Barnes-Wall lattice and some laminated lattices Certain lattice neighboring from Barnes-Wall lattice and some laminated lattices

2009-01-23

arxiv.org/abs/0901.3599v2

Mathematics

Combinatorics

20 pages, 9 figures. http://www2.math.kyushu-u.ac.jp/~j.shigezumi/

Scientific paper

We give classifications of integral lattices which include the Barnes-Wall
lattice $BW_{16}$ or laminated lattices of dimension $1 \leqslant d \leqslant
8$ and of minimum 4. Also, we give certain lattice neighboring from each
lattice. Furthermore, we study spherical designs and the other properties.

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