Codes, groups and designs
主 讲 人 ：Patrick Solé 教授
活动时间：07月15日16时30分
地 点 ：yl23455永利102室
讲座内容：
The adjacency code of a rank three group contains PBIBDs by construction. When we are lucky we obtain a BIBD also known as 2-design. This is the case for instance of the one point stabilizer of PSL(2,41) in its action on the binary QR(41). When we are even luckyer we obtain a 3-design in the extended code. This is the case of the XQR(41) in length 42. By considering known families of rank 3 groups we obtain in that way 111 2-design and nine 3-designs. The supporting codes are constructed by modular representation theory. ( joint works with Bonnecaze and with Rodrigues). Another group action method applies to isodual ternary codes the automorphism group of which admits two orbits on triples (joint work with Shi and Liu.) Interesting examples are provided by Generalized Quadratic Residue codes, a family of abelian codes discussed by van Lint and MacWilliams. Since none of the discussed designs can be explained by the Assmus-Mattson theorem or transitivity arguments, all of this work is based on computer calculations in Magma. Recently a theoretical explanation of the designs in the weight 10 codewords of the XQR(41) was provided by Munemasa based on harmonic weight enumerators.
主讲人介绍：
Patrick Solé received the Ingénieur and Docteur-Ingénieur degrees from the Ecole Nationale Supérieure des Télécommunications, Paris, France, in 1984 and 1987, respectively, and the Habilitation à Diriger Des Recherches from the Université de Nice-Sophia Antipolis, Sophia Antipolis, France, in 1993. He has held visiting positions at Syracuse University, Syracuse, NY, USA, from 1987 to 1989, Macquarie University, Sydney, NSW, Australia, from 1994 to 1996, and Lille University, Lille, France, from 1999 to 2000. Since 1989, he has been a Permanent Member of the CNRS and became the Directeur de Recherche in 1996. He is currently a member of the CNRS Laboratory, I2M, Marseille, France. He is the author of more than 200 journal articles and five books. His research interests include coding theory (codes over rings, quasi-cyclic codes), interconnection networks (graph spectra, expanders), vector quantization (lattices), and cryptography (Boolean functions, pseudo random sequences). He was a co-recipient of the Best Paper Award for Information Theory in 1995, given by the Information Theory Chapter of the IEEE. He was an Associate Editor of the IEEE Transactions from 1996 to 1999.
