On Lattices Generated by Finite Abelian Groups
Copyright policy )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 case 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 Min Sha for the covering radius in the case of the Barnes lattices. Also discussed are properties of the automorphism groups of these lattices.
26 pages
- Pomona College United States
- Claremont Colleges United States
well-rounded lattice, Toeplitz, Cauchy, and related matrices, covering radius, Mathematics - Number Theory, 11H31, 11G20, 11H55, 15A15, 15B05, 52C17, finite abelian group, automorphism group, Metric Geometry (math.MG), Determinants, permanents, traces, other special matrix functions, Toeplitz determinant, Lattice packing and covering (number-theoretic aspects), Curves over finite and local fields, Mathematics - Metric Geometry, FOS: Mathematics, Packing and covering in \(n\) dimensions (aspects of discrete geometry), Mathematics - Combinatorics, Quadratic forms (reduction theory, extreme forms, etc.), Number Theory (math.NT), Combinatorics (math.CO), minimal vector
well-rounded lattice, Toeplitz, Cauchy, and related matrices, covering radius, Mathematics - Number Theory, 11H31, 11G20, 11H55, 15A15, 15B05, 52C17, finite abelian group, automorphism group, Metric Geometry (math.MG), Determinants, permanents, traces, other special matrix functions, Toeplitz determinant, Lattice packing and covering (number-theoretic aspects), Curves over finite and local fields, Mathematics - Metric Geometry, FOS: Mathematics, Packing and covering in \(n\) dimensions (aspects of discrete geometry), Mathematics - Combinatorics, Quadratic forms (reduction theory, extreme forms, etc.), Number Theory (math.NT), Combinatorics (math.CO), minimal vector
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