In this paper we unveil basic properties of a code Γq for digital fingerprinting based on a projective plane of order q. We consider a situation where a coalition of malicious users generates a pirated digital content in which a binary sequence w is embedded subject to the marking assumption. Here, the size of the coalition is assumed to be less than or equal to a known constant c ≥ 2. We evaluate the number of candidates of the coalition that can also generate w subject to the marking assumption. It is shown that the number of such candidates is completely determined as a function of w for the case of c = 2. In addition, we give a sufficient condition under which all the malicious users are correctly identified from w for the case of c ≥ 3. Relationships between Γq and other existing classes of codes are discussed as well.