On Codes with the Identifiable Parent Property

Codes with the Identifiable Parent Property and the Multiple-Access Channel

I. The identifiable parent property and some first results about it If C is a q–ary code of length n and a and b are two codewords, then c is called a descendant of a and b if ct ∈ {at, bt} for t = 1, . . . , n. We are interested in codes C with the property that, given any descendant c, one can always identify at least one of the ‘parent’ codewords in C. We study bounds on F (n, q), the maxima...

Perfect hash families, identifiable parent property codes and covering arrays

Codes with the identifiable parent property for multimedia fingerprinting

Let C be a q-ary code of length n and size M , and C(i) = {c(i) | c = (c(1), c(2), . . . , c(n)) ∈ C} be the set of ith coordinates of C. The descendant code of a sub-code C ′ ⊆ C is defined to be C ′ (1) × C ′ (2) × · · · × C ′ (n). In this paper, we introduce a multimedia analogue of codes with the identifiable parent property (IPP), called multimedia IPP codes or t-MIPPC(n,M, q), so that giv...

On optimal codes with w-identifiable parent property

Let C be a q-ary code of length n and X ⊆ C, then d is called a descendant of X if di ∈ {xi : x ∈ X} for all 1 ≤ i ≤ n. C is said to be a w-identifiable parent property code (w-IPP code for short) if whenever d is a descendant of w (or fewer) codewords, one can always identify at least one of the parent codewords in C. In this paper, we give constructions for w-IPP codes of length w + 1. Furthe...

Prolific Codes with the Identifiable Parent Property

Let C be a code of length n over an alphabet of size q. A word d is a descendant of a pair of codewords x,y ∈ C if di ∈ {xi, yi} for 1 ≤ i ≤ n. A code C is an identifiable parent property (IPP) code if the following property holds. Whenever we are given C and a descendant d of a pair of codewords in C, it is possible to determine at least one of these codewords. The paper introduces the notion ...