Frameproof codes are used to preserve the security in the context of
coalition when fingerprinting digital data. Let Mc,lβ(q) be the largest
cardinality of a q-ary c-frameproof code of length l and
Rc,lβ=limqβββMc,lβ(q)/qβl/cβ. It has
been determined by Blackburn that Rc,lβ=1 when lβ‘1Β (modΒ c),
Rc,lβ=2 when c=2 and l is even, and R3,5β=5/3. In this paper, we
give a recursive construction for c-frameproof codes of length l with
respect to the alphabet size q. As applications of this construction, we
establish the existence results for q-ary c-frameproof codes of length
c+2 and size cc+2β(qβ1)2+1 for all odd q when c=2 and for all
qβ‘4(mod6) when c=3. Furthermore, we show that Rc,c+2β=(c+2)/c
meeting the upper bound given by Blackburn, for all integers c such that
c+1 is a prime power.Comment: 6 pages, to appear in Information Theory, IEEE Transactions o