讲座内容：

In this talk we consider a reconstruction problem which was originally stated in coding theory but it has a combinatorial context. This problem is equivalent to finding the largest intersection of two metric balls of a given radius. We are interested on this problem with respect to permutations under different metrics. First, we give a short overview of some old results. Second, we present some new results for permutations over the Hamming metric. These results are based on a recent work with Xiang Wang.