Lattices and Codes

What it is about

You will learn fundamental types of lattices (e.g., even/odd, unimodular, root lattices) and important properties of root lattices as well as the connection between (binary) linear codes and certain integer lattices. In the end you will be able to geometrically construct codes and derive their properties from the lattice structure and associated theta functions or modular forms.

What you will be able to do

• Know the basic types of lattices
• Understand properties and classification of root lattices
• Describe the relation between (doubly even) self-dual codes and (even) unimodular lattices
• Apply theta functions of lattices and their connection to modular forms
• Explicitly construct codes and derive properties from them

What the module consists of

• VorlesungConveying theoretical content (blackboard lectures)
• ÜbungDeepening through discussion and solving exercises

Teaching method

• TafelvorträgeFor systematic presentation of theory in the lectures
• ÜbungsbesprechungenTo deepen understanding and apply methods to examples