This paper creates a kind of linear independent character code, presents a new theory based on Synergetic, which applies Synergetic to digital fingerprinting, and then proposes a scheme of collusion-resistant digital fingerprinting based on residual characters tracking. The efficiency and the performance are proved and analyzed by theories and examples. The experimental results indicate that the proposed method can greatly improve the efficiencies of encoding and tracing in the digital fingerprinting. The performance in robustness and collusion-resistant is able to meet the requirements of the applications of digital fingerprinting.