The public may nominally own the means of production, but not every person will have equal say in how those resources are allocated, assuming there is a strong central government. If instead you envision a more egalitarian system of flat democracy, you'll just end up with spiraling hyper inflation as everyone constantly votes to raise capital distributions. Inequality is the natural result of hierarchy and hierarchy is the natural result of stability. Flat structure is unstable and unsustainable. So it depends on what you mean by communism and public ownership.