The next meeting of the Mathematical Foundations of Mathematics Seminar will be held on July 5th, 2022, at 2:00 pm (UTC+3) in the Conference Room of IMI-BAS.
Prof. Alexander Barg from the University of Maryland will deliver a lecture on

Remarks on the 1st linear programming bound for binary codes

Abstract: The “linear programming bound” on the rate of binary codes (1977) is a fundamental result in coding theory that continues to attract attention to this day, with new proofs appearing every now and then. I will discuss 2 proofs from about 2006-08, appearing in arXiv:cs/0512025 (Barg-Nogin) and arXiv:math/0702425 (Navon and Samorodnitsky). Both proofs are based on Fourier analytic arguments on the Boolean cube and exhibit interesting parallels and differences (none of them actually uses linear programming). One of the applications enables us to establish upper bounds on the maximum size of binary codes of large distance, d=n/2 – t√n.

Everybody is invited.