 
Summary: Parentidentifying codes
Noga Alon
Eldar Fischer
Mario Szegedy
February 22, 2002
Abstract
For a set C of words of length 4 over an alphabet of size n, and for
a, b C, let D(a, b) be the set of all descendants of a and b, that is, all
words x of length 4 where xi {ai, bi} for all 1 i 4. The code C
satisfies the Identifiable Parent Property if for any descendant of two
codewords one can identify at least one parent. The study of such
codes is motivated by questions about schemes that protect against
piracy of software. Here we show that for any > 0, if the alphabet
size is n > n0( ) then the maximum possible cardinality of such a code
is less than n2 and yet it is bigger than n2 . This answers a question
of Hollmann, van Lint, Linnartz and Tolhuizen. The proofs combine
graph theoretic tools with techniques in additive number theory.
Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel Aviv University, Tel Aviv, Israel. Research supported in part by a USAIsraeli BSF
