You are mistaken as to the difference between socialism and communism. In short, a communism economy is a demand economy where the government not only owns the means of production but decides what and how much to produce with out regards for the market of the goods or services. In a socialist economy the government owns the means of production but uses the market to determine what and how much to produce. That's a big difference. The uses of a demand economy was one of the reasons the USSR failed.
You can not literally go by the name United Soviet Socialist Republics. It is misleading. Hitler call his party the National Socialist German Workers Party. By your reasoning Hitler would have been a communist.
No, I am not mistaken I actually minored in Economics the second time I went to college when I got my second Engineering BA.
The very definition of socialism does not use any elements of a free market economy to determine anything. It is total government control of the economy from startup, production, to distribution the government IS the market in a socalist society.