On Lattices Generated by Finite Abelian Groups

This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In the case where the generating group is cyclic, they are also known as the Barnes lattices. It is shown that for every...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on discrete mathematics 2015-01, Vol.29 (1), p.382-404
Main Authors: Böttcher, Albrecht, Fukshansky, Lenny, Garcia, Stephan Ramon, Maharaj, Hiren
Format: Article
Language:English
Subjects:
Automorphisms
Covering
Exploration
Lattices
Mathematical analysis
Upper bounds
Vectors (mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In the case where the generating group is cyclic, they are also known as the Barnes lattices. It is shown that for every finite Abelian group with the exception of the cyclic group of order four these lattices have a basis of minimal vectors. Another result provides an improvement of a recent upper bound by M. Sha for the covering radius in the case of the Barnes lattices. Also discussed are properties of the automorphism groups of these lattices.
ISSN:0895-4801
1095-7146
DOI:10.1137/140982520