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

Abstract

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

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