题目：On the nonexistence of lattice tilings of Zn by Lee spheres

报告人: 张韬副教授, 广州大学

Abstract: In 1968, Golomb and Welch conjectured that Zn cannot be tiled by Lee spheres with a fixed radius r 2 for dimension n 3. This conjecture

is equivalent to saying that there is no perfect Lee codes in Zn with radius

r 2 and dimension n 3. Besides its own interest in discrete geometry and coding theory, this conjecture is also strongly related to the degree-diameter problems of abelian Cayley graphs. Although there are many

papers on this topic, the Golomb-Welch conjecture is still far from being

solved. In this talk, we introduce some new algebraic approaches to

investigate the nonexistence of lattice tilings of Zn by Lee spheres, which is a special case of the Golomb-Welch conjecture. Using these new methods, we show the nonexistence of lattice tilings of Zn by Lee spheres of the same radius r = 2 or 3 for infinitely many values of the dimension n.

In particular, there does not exist lattice tilings of Zn by Lee spheres of

radius 2 for all 3 n 100 except 8 cases.

时间：4月12日（周五）上午10:20--11:10

地点：首都师大新教2楼   613 教室

欢迎全体师生积极参加！