Maximum two-distance sets in binary codes, Euclidean space and spheres. Function-Like States
- 講者俞韋亘 教授 (中央大學( National Central University))
邀請人：鐘楷閔 - 時間2026-01-14 (Wed.) 15:00 ~ 16:00
- 地點資訊所新館101演講廳
摘要
If a set of finite points such that the distances formed by any two points from the set have two possible values, then we call it a two-distance set. For example, the four points of a square form a two-distance set (since the distances are 1 and square root of 2 after resacaling. We address the problem of maximum size of two-distance sets in binary codes, Euclideas space and unit spheres. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths. We also solved the spherical two-distance sets in almost every dimension. In the end, I will metnion our progress on the maximum two-distance set in Euclidean space (R^n) for n from 9 to 14, and this part is the joint work with Meng-Tsun Tsai and Lee and Sheng.