On noise stability of a system with error-correcting codes

The problem posed in this paper is to give a relation connecting the noise stability of a communication system in which error-correcting codes are used to the parameters of these codes. The amount of code combinations is found, which differ from each other by not less than a given number of elements for a given arrangement of all the possible combinations. It is proved that the quantity depends on the arrangement of the primary combinations. Inequalities are obtained for the greatest amount of combinations , for which any two differ by not less than elements for small and large values of the common number of elements in each code combination. It is established that the probability of distortion, , of a code group in a system with correcting codes satisfies the inequality , where is the probability of distortion of one element. The shape of the function is found for large values of . Graphs of this function are constructed.