The communist system used in the Soviet Union was the polar opposite of a market system.
A market system is based on the idea of personal, economic freedom. People have the right to own private property and they have the right to do more or less whatever they want with that property. People do what they want with their property in hopes of making money and becoming wealthy.
In a communist system, none of this is true. There is no significant private property. People do not control the economic decisions made in the society. Instead, the government controls the economy. It owns all significant property and it makes plans to determine what products will be made in the economy. The profit motive does not exist.
In these ways, the communist system that existed in the Soviet Union is the exact opposite of a market system.