Information reconstruction using minimum number of erroneous patterns and optimization problems of multiple transmission

The problem of effectively reconstructing an unknown object using its patterns distorted by errors of given type and multiplicity is considered. The efficiency of recognition is understood in the sense of minimizing the number N of erroneous patterns that are sufficient for reconstructing an unknown object exactly or with given accuracy and/or with given error probability. This problem essentially differs from the traditional problems of storing and transmitting encoded messages, because we consider reconstruction of an arbitrary object from a given set. In this paper the problem is formulated in terms of metric spaces, and it is solved for metric spaces that are most interesting for the theory of information transmission. For these metric spaces, the minimum numbers of erroneous patterns are obtained, and simple algorithms for reconstructing objects using these minimum numbers of patterns are presented