Lattices from elliptic curves over finite fields

11/19/2013 - 12:15pm
11/19/2013 - 1:10pm
Speaker: 
Hiren Maharaj
Abstract: 

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 talk we will discuss 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 discuss a bound on the covering radii of these lattices, which improves on the standard inequalities.

Where: 
Mudd Science Library 126, Pomona College