Article - postprint
Claremont McKenna College, Mathematics (CMC)
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.
© 2014 Fukshansky, Maharaj
Fukshansky, Lenny, Hiren Maharaj, "Lattices from elliptic curves over finite fields" Finite Fields and Their Applications, vol. 28 (July 2014), pg. 67--78.