Projective Reed Muller Codes constitute an interesting class of linear codes, which was introduced by Gilles Lachaud in 1988. Questions about their minimum distance are intimately related to the question about the maximum possible number of F-rational points in the m-dimensional projective space on a hypersurface of degree d in m+1 variables with coefficients in a finite field F. Michael Tsfasman gave a conjectural formula for this maximum possible number of points on such hypersurfaces, and the conjecture was soon proved in the affirmative by Jean-Pierre Serre. In all these works, it is generally assumed that the degree d is at most q, where q is the number of elements in F. Anders Sørensen considered in 1991 more general projective Reed Muller codes where d can be larger than q. From a coding theoretical perspective, it is more natural to consider this larger class. Sørensen proposed a formula for the minimum distance in the general case, and also studied the duals of the projective Reed-Muller codes.
We shall revisit the work of Sorensen by pointing out some minor inaccuracies in his proof of the minimum distance. We then propose an alternative proof. Further, we address the question of obtaining a characterization of the minimum weight codewords of projective Reed Muller codes.
This is a joint work with Rati Ludhani. [-]

Private information retrieval (PIR) addresses the question of how to retrieve data items from a database or cloud without disclosing information about the identity of the data items retrieved. The area has received renewed attention in the context of PIR from coded storage. Here, the f iles are distributed over the servers according to a storage code instead of mere replication. Alongside with the basic principles of PIR, we will review recent capacity results and demonstrate the usefulness of the socalled star product PIR scheme. The talk is based on joint work with Ragnar Freij-Hollanti, Oliver Gnilke, Lukas Holzbaur, David Karpuk, and Jie Li.[-]

APN and AB functions are S-boxes with optimal resistance to the linear and differential cryptanalysis. In this talk we survey known constructions and classifications of these functions and discuss big open problems for the monomial case. Among these problems are the Dobbertin's conjecture on nonexistence of new APN monomials (open since 2000), the Walsh spectrum of Dobbertin's APN monomials (open since 2000), the existence of APN permutations of the form $x^d+L(x)$ where $x^d$ is some of the known APN monomials and $L$ is a nonzero linear map.

Remark :
On page 18 the speaker refers the classification result by Brinkmann [3] for functions from the field $F_{2^4}$ of order 16 to itself.[-]