On Lattices Generated by Finite Abelian Groups

Authors

Albrecht Böttcher, Technische Universitat Chemnitz
Lenny Fukshansky, Claremont McKenna CollegeFollow
Stephan Ramon Garcia, Pomona CollegeFollow
Hiren Maharaj, Pomona College

Document Type

Article - postprint

Department

Mathematics (CMC), Mathematics (Pomona)

Publication Date

2015

Abstract

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.

Rights Information

© 2015 Society for Industrial and Applied Mathematics

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1137/140982520

Recommended Citation

Boettcher, A., Fukshansky, L., Garcia, S., Maharaj, H. On lattices generated by finite Abelian groups, SIAM Journal on Discrete Mathematics, vol. 29 no. 1 (2015), pg. 382--404.