Construction of a Primary Source Code with Given Code Distances Between Adjacent Code Combinations

During primary encoding, the elements of the original message are assigned certain numbers, usually in binary form. The code combinations of n binary symbols formed in this way differ from each other by a certain code distance di,j. Most often, a weighted (natural) code, as well as a Gray code, are used as primary coding methods in cases where it is required that between all adjacent code combinations there be a code distance equal to one. This requirement follows from the assumption that one-time errors most often occur, which is not always true. Therefore, in these situations, a different distance between adjacent primary coding code combinations is required, which is the subject of research in this article.