In mass storage systems or certain transmission channels, such as optical data storage and non-volatile memory (flash), noise or interference is not the only disturbance during the data transmission, the error performance sometimes can be seriously degraded by the phenomena of unknown channel offset (drift) or gain mismatch, this is because the conventional minimum Euclidean distance decoding, where the receiver picks a codeword from the code book to minimise the Euclidean distance with the received codeword, doesn't offer resistance for the offset and gain mismatch. As a alternative to the minimum Euclidean distance detection, a new distance called Pearson distance and the Pearson-distance-based detection are introduced by Immink and Weber, where the error performance is immune to unknown offset and/or gain mismatch but more sensitive to the noise than the traditional Euclidean distance detection. In addition, the Pearson-distance-based decoding can only productively used for sets of q-ary codewords with some specific properties, which is a new class of code called Pearson code. Therefore, to make the Pearson-distance-based detection more applicable against the channel noise, it is crucial to improve the error control capabilities of Pearson code. In this thesis, we will investigate the performance of different Pearson codes in the Pearson-distance-based detection for offset-only mismatch case and offset-and-gain mismatch case. We will analyze the factors that can reflect or affect the performance of the Pearson code by studying the relations between Pearson distance and Hamming distance. The simulation results will be compared and discussed, the advices for improving the error control capability of the Pearson code will be given according the factors we found.