Permutation decoding for codes from designs, finite geometries and graphs

The method of permutation decoding was first developed by MacWilliams in the early 60’s and can be used when a linear code has a sufficiently large automorphism group to ensure the existence of a set of automorphisms, called a PD-set, that has some specifed properties. These talks will describe some recent developments in finding PD-sets for codes defined through the row-span over finite fields of incidence matrices of designs or graphs, or adjacency matrices of regular graphs, since these codes have many properties that can be deduced from the combinatorial properties of the designs or graphs, and often have a great deal of symmetry and large automorphism groups.