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A notion of bent sequences based on Hadamard matrices

发布时间:2023-09-05 作者: 浏览次数:
Speaker: Professor Patrick Sole DateTime: 2023年9月16日(周六)下午14:30-15:30
Brief Introduction to Speaker:

Professor Patrick Solé received the Ingénieur and Dr.-Ing. degrees from Ecole Nationale Supérieure des Télécommunications, Paris, France, in 1984 and 1987, respectively, and the Habilitation á Diriger des Recherches from Université de Nice Sophia Antipolis, Sophia Antipolis, France, in 1993. He has held visiting positions with Syracuse University, Syracuse, NY, USA, from 1987 to 1989; Macquarie University, Sydney, Australia, from 1994 to 1996; and Lille University, Lille, France, from 1999 to 2000. Since 1989, he has been a permanent member of CNRS, where he was a Senior Scientist, in 1996. He is currently a member of the CNRS Lab, I2M, Marseilles, France. His research interests include coding theory (codes over rings and quasi-cyclic codes), interconnection networks (graph spectra and expanders), vector quantization (lattices), and cryptography (Boolean functions and pseudorandom sequences).


Place: 6号楼M323
Abstract:A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application ( Sol\'e et al, 2021). We study the self dual class in length at most $196.$ We use three competing methods of generation: Exhaustion, Linear Algebra and Groebner bases. Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples. We conjecture that if $v$ is an even perfect square, a self-dual bent sequence of length $v$ always exist. We introduce the strong automorphism group of Hadamard matrices, which acts on their associated self-dual bent sequences. We give an efficient algorithm to compute that group. A generalization to complex Hadamard matrices is sketched out. Talk based on joint work with Wei Cheng, D. Crnkovi\'c, Yaya Li, Denis Krotov, Minjia Shi.