Improved Constructions of Frameproof Codes

Frameproof codes are used to preserve the security in the context of coalition when fingerprinting digital data. Let M
_c,l
(q) be the largest cardinality of a q-ary c-frameproof code of length l and R
_c,l
=lim
_q→∞
M
_c,l
(q)/q
^{[ l/c]}
. It has been determined by Blackburn that R
_c,l
=1 when l≡1(mod c), R
_c,l
=2 when c=2 and l is even, and R
_3,5
=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 c+2/c(q-1)
²
+1 for all odd q when c=2 and for all q≡4 when c=3 . Furthermore, we show that R
_c,c+2
=(c+2)/c meeting the upper bound given by Blackburn, for all integers c such that c+1 is a prime power.