Rate vs. Distance – Milestones and Obstacles Towards Improved Bounds

Title: Rate vs. Distance – Milestones and Obstacles Towards Improved Bounds

Abstract: The rate vs. distance problem is a major open problem of coding theory. Significant progress has stalled since 1977. The best-known upper bound, established by MRRW, is derived from Delsarte’s reformulation of the combinatorial question as a linear program (LP). This breakthrough sparked a line of research into stronger optimization problems. However, the more powerful formulations have remained difficult to analyze, and no improved bounds have been achieved yet. In this talk, I will present new results on the analysis of a recently developed LP hierarchy. I will discuss the techniques employed, current limitations, and possible strategies to deal with these challenges.