• Multi antena system. Numerical study of optimal configuration for the product distance (September 09)
  • Work on the asymptotic improvement of the Gilbert Varshamov bound. (October 09-April 09)

- Study with the general linear group. Counting. (October 09)

-Extension of the GV improvement by Gaborit and Zemor to other techniques ? Application to rank metrics. (February 10)

-Learn about graph entropy in connection with Gilbert-Varshamov bound (March 10).

-Research on automorphism groups of Generalised Quadratic residue codes. (April 10)

  • Work on lattice reduction with Seth Flaxmann. How to combine different informations from approximate short vector / reduced lattice to derive the shortest vector ? (Octobre 09 - January 10)
  • Work on w-witness set. Construction of counter-example to the case w=n/2. Proof of conjecture by Cohen et al. when n=5, w=2. Attempt to apply SDP program for bounds. (January 10)
  • Application of SDP bounds on permutations code with Terwilliger algebra. (cf. articles by Cameron) Computation of zonal function (= characters of symetric group). Turns out it's already done by Tarnanen (June 10)
  • Research on exceptional units, i.e. units u such that 1-u is also a unit. Application to space time codes ? Cf. articles by Lenstra, Houriet (Juillet 10)
  • Explicit LDPC from Caley graphs (July 10-August 10).

Learn how to compute irreducible represention of finite p-groups Theory of monomial group and irreducible representation Generation of all p-groups of a certain order (August).

  • Decoder for mimo code. (September 10)

Wimax standard. Work with Oussama Damen

  • Theory of expander groups (October 10)
  • Witness set. Study of the representations of the space F2^n times Jw where Jw is the Johnson space under the action of the hyperoctaedral group. Numerical construction of the zonal functions. SDP program and first bounds on the size of a w-witness set. Bounds turns out to be sharp. (Nov 10 -Feb 2010)
  • Winter school “Group action in number theory” (18 - 28 Jan 2011)