Seminar: Lattices and Codes

We are reading Lattices and Codes  by Wolfgang Ebeling
 
Topics
 
Topic are assigned by the first come first served principle.
You should come talk to me 2 weeks before your talk, to discuss it.
 
  1. Introduction to lattices and codes
  2. Linear Codes  & codes to lattices
  3. Root lattices
  4. Classification of root lattices
  5. Irreducible root lattices and binary codes
  6. The highest root and Weyl vector
  7. Theta function of a lattice and the modular group
  8. Introduction to modular forms
  9. The algebra of modular forms
  10. The weight enumerator of a code
  11.  The extended Golay code, the MacWilliams Identity & Gleasons Theorem
  12. Root systems in even unimodular lattices and a classification result
  13. Overlattices, codes an classification results
Literature
  • W. Ebeling: Lattices and Codes, 3rd ed., Adv. Lect. in Math., Springer Spektrum 2013.
  • H.  Conway,  N.J.A. Sloane: Sphere  Packings,  Lattices  and  Groups,  3rd  ed., Springer-Verlag 1999
Dates
Tuesdays 10:15 - 11:45, E2.5 SR 1
 
Prerequisites
Linear Algebra I & Analysis I
Depending on the topic of your talk
Algebra and complex analysis may of use.
 
 
Scheinkriterien
  • regular, active participation in the seminar
  • a successful talk (90 minutes)
  • if you need 7 credit points, you have to hand in a written exposé of your talk (3-5 pages).