Linear Programming and Semidefinite Programming in Coding Theory - An Incomplete Overview

Explore the evolution and applications of Delsarte's linear programming method in a 51-minute lecture by Alexander Barg from the University of Maryland. Delve into the development of the MRRW bound for binary codes and its subsequent improvements by Levenshtein. Examine the method's extension to spherical codes and metric spaces with distance-transitive group actions. Discover connections to combinatorial objects like few-distance sets, equiangular lines, strongly regular graphs, and tight frames. Learn about three-point bounds for codes and their impact on kissing numbers and sphere packings. Follow quick proofs of the MRRW and Levenshtein bounds, leading to the Cohn-Elkies bound for sphere packings. Gain insights into recent advancements in equiangular lines, codes with few distances, energy bounds for codes, and their relationship to smoothing of codes and uniform distributions.