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Mathematics > Number Theory

arXiv:1401.2434 (math)
[Submitted on 10 Jan 2014 (v1), last revised 12 Feb 2014 (this version, v2)]

Title:Lattices from elliptic curves over finite fields

Authors:Lenny Fukshansky, Hiren Maharaj
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Abstract:In their well known book Tsfasman and Vladut introduced a construction of a family of function field lattices from algebraic curves over finite fields, which have asymptotically good packing density in high dimensions. In this paper we study geometric properties of lattices from this construction applied to elliptic curves. In particular, we determine the generating sets, conditions for well-roundedness and a formula for the number of minimal vectors. We also prove a bound on the covering radii of these lattices, which improves on the standard inequalities.
Comments: 10 pages, to appear in Finite Fields and Their Applications; some minor revisions and improvements in this version
Subjects: Number Theory (math.NT)
MSC classes: 11H06, 11G20
Cite as: arXiv:1401.2434 [math.NT]
  (or arXiv:1401.2434v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1401.2434
Journal reference: Finite Fields and Their Applications, vol. 28 (July 2014), pg. 67--78

Submission history

From: Lenny Fukshansky [view email]
[v1] Fri, 10 Jan 2014 19:42:37 UTC (11 KB)
[v2] Wed, 12 Feb 2014 05:38:38 UTC (11 KB)
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