Fast calculation algorithm of the undetected errors probability of CRC codes

The error detecting functions of linear block code can be realized via simple software or hardware. The error detection, which includes long-term theoretical research and many good properties, is often applied widely in digital communication and data storage. The weight distribution of linear block code and its dual code are important parameters of calculating the probability P_ud of undetected errors. Further, cyclic redundancy check (CRC) codes and Bose, Chaudhuri and Hocquenghem (BCH) cyclic codes are subclasses of linear block codes. This paper proposes a fast calculation algorithm of weight distribution of the dual code which outperforms those of previous studies in time complexity, and the probability of undetected error of different CRC codes standards under various codeword lengths are also simulated efficiently.