A hypergraph approach to the identifying parent property: the case of multiple parents

Let C be a code of length n over an alphabet of q letters. A word y is called a descendant of a set of t codewords x1,…,xt if yiε{xi1,…,xit} for all i=1,…,n. A code is said to have the identifiable parent property if for any n-word that is a descendant of at most t parents it is possible to identify at least one of them. We prove that for any t <= q−1 there exist sequences of such codes with asymptotically nonvanishing rate.