SPHERICAL DESIGNS FROM THE NORM-3 SHELL OF INTEGRAL LATTICES

Author:

Shigezumi Junichi1

Affiliation:

1. Graduate School of Mathematics, Kyushu University, Fukuoka, Japan

Abstract

A set of vectors all of which have a constant (non-zero) norm value in a Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum 3 (Réseaux et "designs" sphérique, 2001), whose minimal shell is a spherical 5-design. This note considers the classification of integral lattices whose shells of norm 3 are 5-designs.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Reference5 articles.

1. Sphere Packings, Lattices and Groups

2. Spherical codes and designs

3. R. Mation and A. Rosa, The CRC handbook of combinatorial designs, 2nd edn. (CRC Press, Boca Raton, FL, 2006) pp. 25–58.

4. A note on odd unimodular Euclidean lattices

5. SHELLS OF SELFDUAL LATTICES VIEWED AS SPHERICAL DESIGNS

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