If two people want to possess the same physical object simultaneously, a conflict arises, which is resolved by establishing property rights.

Сode is infinitely reproducible.

If you copy my file, I do not lose the original.

Since no physical conflict arises from the use of an idea, there is no basis to call it "property" in the classical sense.

Or... just... don't publish it, make it proprietary and I won't use it.

Theft implies depriving an owner of their physical asset. When copying ("piracy") occurs, the owner does not lose their copy.

So... nope, it's not communism.