Some new p-ary two-secure frameproof codes

If C is a p-ary code of length n and a⁽¹⁾ and a⁽²⁾ are two codewords, then a⁽³⁾ is called a descendant of a⁽¹⁾ and a⁽²⁾ if a_i⁽³⁾ ∈ {a_i⁽¹⁾, a_i⁽²⁾} for i = 1,…, n. We are interested in codes C with the property that either any two nonintersecting coalitions of size 2 have no common descendant or the descendant of any coalition of size 3 does not belong to the code. We construct such codes based on Hadamard matrices.