THE SMALLEST BASE OF k−SETS
Tóm tắt
In information theory, especially in storage model, private sharing, encryption, etc. sometimes we want to distribute a given database into many small parts, each of which is stored by a party in such a way that when there are a cooperation of sufficient number of parties, then it is enable to recover the original information. For this purpose, the paper describes the way to work on a given finite set then construct a family of uniform subsets such that there exists only one permutation that maps one-to-one each subset. Of course, the optimality of construction will be considered through its size. By evaluating the number of occurrences of each element in the subsets, it is possible to establish the lower bound for that size and using the simple undirected graph to model. The construction step is only successful with relevant data and the general case is under further study.