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 maximal cardinality of a code C with this property, which we call the identifiable parent property. Such codes play a role in schemes that protect against piracy of software. They have been introduced by Hollmann, van Lint, Linnartz and Tolhuizen [9]. We repeat first their concepts, basic examples and results. Consider a code C of length n over an alphabet Q with |Q| = q (i.e., C ⊂ Q). For any two words a, b in Q we define the set of descendants D(a, b) by