报告人:周悦副教授 (中国人民解放军国防科技大学)
时间:2021/07/01 10:00-11:00
地点:腾讯会议 ID:842 663 916
报告摘要:
More than 50 years ago, Golomb and Welch conjectured that there is no perfect Lee codes C of minimum distance 2r + 1 in Z^n for r >=2 and n >= 3. Recently, Leung and the speaker [1] proved that if C is linear, then Golomb-Welch conjecture is valid for r = 2 and n >= 3. In this talk, we consider the classication of linear Lee codes with the second best possibility, that is the density of the lattice packing of Z^n by Lee spheres S(n; r) equals \frac{|S(n,r)|}{|S(n,r)|+1}.
We show that this packing density can be achieved for r = 2 if and only if n = 1; 2. To achieve this goal, we also have to check the associated group ring equations. However, the technique applied here is almost completely dierent from the one used in [1].
[1] K. H. Leung and Y. Zhou. No lattice tiling of Zn by Lee sphere of radius 2. Journal of Combinatorial Theory, Series A, 171:105157, 2020.
邀请人:季利均、汪馨