Sudhir GHORPADE
Summary: The course covered the following topics:
Linear Codes associated to higher dimensional varieties:
Geometric approach to linear codes via the language of projective systems. The following specific classes of linear codes and some of their fundamental properties including determination of basic parameters will be discussed.
- Codes associated to Veronese varieties (Projective Reed-Muller Codes)
- Grassmann codes
- Schubert codes
Betti numbers of linear codes and matroids:
Matroids and simplicial complexes associated to linear codes. Graded minimal free resolutions and Betti numbers of Stanley-Reisner rings of these simplicial complexes. Relations with generalized Hamming weights and generalized weight enumerator polynomials of linear codes