Some instances of the template matching problem, primarily for binary images corrupted with spatially white binary symmetric noise, are studied. We use the pixel-valued image data as well as data coded by two simple schemes, a modification of the Hadamard basis and the coarsening of resolution. Bayesian matching rules residing on M-ary hypothesis tests are developed. The performance evaluation of these rules is studied. This approach to the matching problem is intended to show the trade- off between the quantization and external noise with respect to the ability of detecting an object of the image. We consider the case of the black square template in white background or without known background as well as synthetic template without known background. We call external noise the noise generated at the moment we receive the uncoded image, in which case we have a "corrupt-code-detect system," or the noise coming as the effect of the transmission of the coded image over a noisy channel, in which case we have a code-corrupt-detect system. In both cases the noise is assumed to be white. The sum-of-pixels and the histogram statistics are introduced in order to overcome the computational load induced by the correlation statistic with the penalty of an augmented probability of false alarm rate. What is intended to be shown in the present work is the usefulness and ability of combining an image coding technique with an algorithm for extracting some "base" information used in image understanding. Numerical and simulation results are given.