Explicit Construction of Secure Frameproof Codes

Γ is a q-ary code of length L. A word w is called a descendant of a coalition of codewords w(1), w(2), . . . , w(t) of Γ if at each position i, 1 ≤ i ≤ L, w inherits a symbol from one of its parents, that is wi ∈ {w i , w (2) i , . . . , w (t) i }. A k-secure frameproof code (k-SFPC) ensures that any two disjoint coalitions of size at most k have no common descendant. Several probabilistic methods prove the existance of codes but there are not many explicit constructions. Indeed, it is an open problem in Staddon et al [11] to construct explicitly q-ary 2-secure frameproof code for arbitrary q. In this paper, we present several explicit constructions of q-ary 2-SFPCs. These constructions are generalisation of the binary inner code of the secure code in Tô et al [14]. The length of our new code is logarithmically small compared to its size. AMS Subject Classification: 68R05, 94A60, 05B99