Preface: Geometric and algebraic combinatorics

Abstract

The present issue of Designs, Codes and Cryptography is devoted to the theme “Geometric and Algebraic Combinatorics”. A central concept in this research area is the Association Scheme. On one hand it can be a tool for a better understanding of combinatorial objects, such as error correcting codes, block designs, point-line incidence geometries, and permutation groups. On the other hand, many association schemes are interesting objects in themselves. This includes the strongly regular and distance-regular graphs. Algebraic tools like eigenvalues are extremely important for studying association schemes, but are also useful tools in their own right for studying the structure of graphs. Also incidence geometries, especially projective and affine geometries over finite fields are often related to association schemes, but as expected, here geometric methods play a more important role. The issue contains fourteen articles, which we’ll briefly review.