Partially correct, until you get to the individual. Note that this isn't an endorsement of communism, just clarification because a lot of people use the word without understanding it properly. Communism is largely about the means of production, the spaces, tools, and materials requires to produce the things society needs. Personal possessions aren't strictly banned under the ideology. Owning your own home, for example, isn't forbidden under communism, but there may be examples of attempted communist states that made laws to the contrary. 

 But if you can't choose what to do with your time & labor then you don't own yourself. People are actually the source of all wealth & production, so if you (as an individual) don't get to decide what you produce & you can't own the tools needed to do so, then communism is ultimately just a philosophy crafted to sell slavery to the slaves. 

 Communism is mass public slavery