Permutation decoding for codes from designs, finite geometries and graphs

Permutation decoding was introduced by MacWilliams [Mac64] in the early 60’s. It 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. This series of talks will describe the method and some recent developments in finding PD-sets for codes defined through the row-span over finite fields of incidence matrices of classes of designs or graphs, and adjacency matrices of classes of regular graphs. 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. J.D.Key (keyj@clemson.edu) Permutation decoding ASI Croatia June 2010 2 / 81

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