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Higher-order Delsarte linear programs for codes and packings
Algebra & Discrete Mathematics| Speaker: | Chris Jones, UC Davis |
| Location: | 2112 MSB |
| Start time: | Mon, Apr 27 2026, 2:00PM |
Description
As n goes to infinity, what is the largest rate of an error-correcting code in {0,1}^n, or the highest density of a sphere packing in R^n? Upper bounds for these two problems were proven in the 1970s using Delsarte's linear programming method and the theory of association schemes. However, the exponential gap between the upper and lower bounds has not moved in the intervening 50 years. In recent work, we proposed a new hierarchy of linear programs which refines the Delsarte linear programs. I will discuss some of our results on these linear programs, and speculate on what is needed to improve the upper bounds.