学术科研-【科学大讲堂】How small can the aperiodic autocorrelations of a binary sequence be?

学术科研

数学大讲堂

【科学大讲堂】How small can the aperiodic autocorrelations of a binary sequence be?

演讲者：Jonathan Jedwab（西蒙菲莎大学）
时间：2025-12-02 16:30-17:30
地点：理学院大楼M1001

Abstract

Binary sequences whose aperiodic autocorrelations are collectively small have been sought since the 1950s as modulating signals in digital communications. Two popular measures of smallness are the merit factor and the peak sidelobe level. Studies of these two measures, often motivated by numerical experiments, involve diverse mathematical tools including Fourier analysis, estimation of character sums, estimation of the number of lattice points in polyhedra, finite fields, and probabilistic methods. Despite a large and growing body of theory, numerical experiments suggest that there are unexplained infinite families of binary sequences having record asymptotic merit factor or peak sidelobe level.

I shall describe the merit factor problem and peak sidelobe level problem from scratch, outline their history, and explain the intriguing numerical experiments whose results await explanation.

Biography

Jonathan Jedwab received the B.A. degree in mathematics and the Diploma degree in mathematical statistics from Cambridge University, UK in 1986 and 1987, respectively, and the Ph.D. degree in mathematics from the University of London, UK in 1991. He spent 14 years at the Mathematics Consultancy Group, Hewlett-Packard Laboratories, UK. Since 2003, he has been with the Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada. His research interests include combinatorial design theory, often motivated by practical problems of digital communications engineering.