Modern communication systems tend to use different channel codes to find a balance between communication speed and quality. Accordingly, the blind identification techniques of encoders have drawn much research interest. In this letter, we propose a blind identification scheme for the Low-Density Parity Check (LDPC) coded communication systems based on a known candidate set. The proposed scheme can adaptively adjust the length of the received sequence to approach an arbitrary probability of missed detection and false alarm for codes in the candidate set, where the latter probability has received little attention by the existing methods. On this basis, the proposed scheme can determine whether there are unknown codes in the received vector, which is useful in practical applications. The performance of the proposed scheme is investigated using system simulations.