Theadjacency code of a rank three group contains PBIBDs by construction. When weare lucky we obtain a BIBD  also known as 2-design. This is the casefor instance of  the one point stabilizer of PSL(2,41) in its action onthe binary  QR(41). When we are even luckyer we obtain a 3-design inthe extended code.  This is the case of the XQR(41) in length 42. Byconsidering known families of rank 3 groups we obtain in that way 111 2-designand nine  3-designs. The supporting codes are constructed by modularrepresentation theory. ( joint works with Bonnecaze and with Rodrigues). Anothergroup action method applies to isodual ternary codes the automorphism group ofwhich admits two orbits on triples (joint work with Shi and Liu.) Interestingexamples are provided by Generalized Quadratic Residue codes, a family ofabelian codes discussed by van Lint and MacWilliams. Since none of thediscussed designs can be explained by the Assmus-Mattson theorem ortransitivity arguments, all of this work is based on computer calculationsin Magma. Recently a theoretical explanation of the  designs in the weight10 codewords of the XQR(41) was provided by Munemasa based on harmonic weightenumerators.

PatrickSolé received the Ingénieur and Docteur-Ingénieur degrees from the EcoleNationale Supérieure des Télécommunications, Paris, France, in 1984 and 1987,respectively, and the Habilitation à Diriger Des Recherches from the Universitéde Nice-Sophia Antipolis, Sophia Antipolis, France, in 1993. He has held visitingpositions at Syracuse University, Syracuse, NY, USA, from 1987 to 1989,Macquarie University, Sydney, NSW, Australia, from 1994 to 1996, and LilleUniversity, Lille, France, from 1999 to 2000. Since 1989, he has been aPermanent Member of the CNRS and became the Directeur de Recherche in 1996. Heis currently a member of the CNRS Laboratory, I2M, Marseille, France. He is theauthor of more than 200 journal articles and five books. His research interestsinclude coding theory (codes over rings, quasi-cyclic codes), interconnectionnetworks (graph spectra, expanders), vector quantization (lattices), andcryptography (Boolean functions, pseudo random sequences). He was aco-recipient of the Best Paper Award for Information Theory in 1995, given bythe Information Theory Chapter of the IEEE. He was an Associate Editor of theIEEE Transactions from 1996 to 1999.