Features of Bijection of Spaces when Transmitting Messages from Source to Recipient

Signals from the source of messages can be different, and to describe them, appropriate models are used, which make it possible to represent the generated signals in various metric spaces that are adequate to the type of signals under consideration. For example, the Euclidean space is used to describe analog signals, while the Hamming space is used to describe a discrete digital signal. The article discusses the features of bijections of the Hamming and Euclidean spaces. Matrices of code distances for the Gray and Natural codes are constructed. Tables of distortions in code combinations and tables of transitions of code combinations from one to another for two types of coding are given. The results obtained show certain advantages of the Gray code in comparison with the Natural code.