On a cyclic sequence of a packing by triples with error correcting consecutive unions

Abstract

In this paper, we investigate a set-sequence containing k-subsets of a v-set as elements such that the collection of all involved k-subsets and unions of all two consecutive k-subsets of this sequence forms an error correcting code with minimum distance d. Such a sequence is called a cyclic sequence with error correcting consecutive unions, and said to be maximal if the number of k-subsets contained in the sequence is maximum for given k, d and v. In particular, we treat the case of k = 3 and d = 3, and give an explicit construction of such a sequence for every v ≥ 10 by utilizing a packing design by triples. This kind of combinatorial structure is motivated from applications in combinatorial group testing.