Lenny Fukshansky, Hiren Maharaj
Published 2014-01-10, updated 2014-02-12Version 2
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
Journal: Finite Fields and Their Applications, vol. 28 (July 2014), pg. 67--78
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