Weighted perfect codes in Lee metric

In this talk, we will present results about perfect weighted coverings of radius 1 in the Lee metric. Weighted coverings are a very natural generalization of many classes of codes. Perfect weighted coverings are well studied in the Hamming metric, but also in other contexts with different names, such as regular-sets, multiple coverings or [a, b]-dominating sets. In this talk, we present results of existence as well as of non-existence for perfect weighted coverings of radius one on the multidimensional grid graphs.