## Lattice ideals and coding theory

#### Hiram Lopez Valdez – Clemson University

By issues of the destiny, in the world of mathematics there are two (at least) different objects called “lattices”. One of them is related with the concept of an ordered set and we will not talk about this one. Another object which is also called a lattice is just defined as a subgroup of Z^n. Given a lattice L, we associate a binomial ideal I(L) called “lattice ideal”.

We will study some of the main properties of lattice ideals, for instance given a set of generators of L, how to find I(L), and given a set of generators of I(L), how to find L. We will see also how to identify if an arbitrary binomial ideal comes from a lattice, and if this is the case, how to find such a lattice.

Finally, we will see how we can apply lattice ideals to coding theory.