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In this paper, we present a new algorithm of blind frame synchronization and phase offset estimation that can be applied to any digital transmission scheme using a channel coding with a binary phase shift keying (BPSK) modulation. The estimator is based on the calculation of the syndrome elements of a received codeword obtained using the parity check matrix of the code. After presenting the proposed method, we evaluate its performance by applying it to some low density parity check (LDPC) codes and convolutional codes. This performance is measured by plotting the probability of false frame synchronization and the mean squared estimation error (MSEE) versus the signal to noise ratio (Eb/N0).