N. I. Chervyakov, A. A. Yevdokimov

The associative neural network calculating Lee distance is considered. The neural network allows defining in real time the closest pattern. The developed neural network allows us to find out and correct errors which rates are defined by the number of the control bases; to find out and correct the errors which rate exceeds possibilities of redundancy RNS, but it is possible thanks to the assumption of high probability of errors of small weight; to receive the list of vectors from a working range located on identical distance from an entrance vector that is required at correction of errors of the big rate and the big weight. Whether use of a neural network probably in tasks of phase-coded signals with imposing additive Gauss noise when probability of that noise will translate a symbol in a symbol close on a phase, is higher, than in a symbol with a very different phase. Whether in case of an error of redundancy insufficient for correction the neural network gives possibility of reception of the limited list of the most probable sets of deductions from a working range. As the received list is limited also range is very small, considered neural network can be used for correction of multimedia data (images and video). In multimedia appendices change of color of pixel on one or two units from true value as a result of decoding will not lead to impossibility of recognition of the image. Distance calculation it will be in real time useful and to high-efficiency computing systems with toroidal topology.