You explicitly said "Communism in the formal sense". You were wrong with that.
Most ideologies and political or economic ideas have had their names subverted to mean something different by opponents (democracy, republicanism, communism, anarchism, capitalism...). That doesn't mean that if you speak in the "formal sense" you can decide to use whatever meaning you prefer.
Most ideologies and political or economic ideas have had their names subverted to mean something different by opponents (democracy, republicanism, communism, anarchism, capitalism...). That doesn't mean that if you speak in the "formal sense" you can decide to use whatever meaning you prefer.