Lattices from Elliptic Curves over Finite Fields

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow
Hiren Maharaj, Clemson University

Document Type

Article - postprint

Department

Claremont McKenna College, Mathematics (CMC)

Publication Date

7-2014

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

Source: Author's post-print manuscript in PDF.

Rights Information

© 2014 Fukshansky, Maharaj

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Recommended Citation

Fukshansky, Lenny, Hiren Maharaj, "Lattices from elliptic curves over finite fields" Finite Fields and Their Applications, vol. 28 (July 2014), pg. 67--78.