Construction of the Primary Code with the Specified Code Distances between Adjacent Code Combinations

During the primary coding, certain numbers are assigned to the elements of the original message, usually in binary form. Thus formed code combinations of
$n$
binary symbols differ from each other by a certain code distance
$d_{ij}$
. Among the most well-known methods of primary coding, we note the weighted (natural) code and the Gray code. The purpose of this article is to develop a method for constructing a primary code with given code distances between adjacent code words. This article also discusses the problem of choosing a primary coding method from the point of view of minimizing distortion of the restored continuous signal under the influence of interference in the communication channel and the occurrence of errors caused by them in the discrete signal.