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

2009/01/23 by Junichi Shigezumi, Shigezumi, Junichi
Computer Science · Materials Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Quasicrystal Structures and Properties #math.CO #msc:03G10 #msc:05B30

paper · pdf · doi:10.48550/arxiv.0901.3599

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

arxiv created 2009/01/24 · arxiv updated 2009/12/01

Abstract

We give classifications of integral lattices which include the Barnes-Wall lattice BW₁₆ 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.

Related

• On 3-lattices and spherical designs
• Midwest cousins of Barnes-Wall lattices
• Dense lattices in low dimensions
• The Leech lattice and other lattices
• Laminating lattices with symmetrical glue