NDLI: On Lattices Generated by Finite Abelian Groups

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Böttcher, Albrecht Garcia, Stephan Ramon Maharaj, Hiren Fukshansky, Lenny
Copyright Year	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.
Starting Page	382
Ending Page	404
Page Count	23
File Format	PDF
ISSN	08954801
DOI	10.1137/140982520
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	29
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-02-12
Access Restriction	Subscribed
Subject Keyword	minimal vector Toeplitz, Cauchy, and related matrices Quadratic forms Lattice packing and covering automorphism group well-rounded lattice Determinants, permanents, other special matrix functions finite Abelian group covering radius Packing and covering in $n$ dimensions Curves over finite and local fields Toeplitz determinant
Content Type	Text
Resource Type	Article
Subject	Mathematics

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