Various embodiments of the present invention provide systems and methods for flaw scan in a data processing system. As one example, a data processing system is disclosed that includes a data detector circuit, a bit sign inverting circuit, and an LDPC decoder circuit. The data detector circuit receives a verification data set that is an invalid LDPC codeword, and applies a data detection algorithm to the verification data set to yield a detected output. The bit sign inverting circuit modifies the sign of one or more elements of a first derivative of the detected output to yield a second derivative of the detected output. The second derivative of the detected output is an expected valid LDPC codeword. The LDPC decoder circuit applies a decoding algorithm to the second derivative of the detected output to yield a decoded output.