Where are justices opinions are written?

Certain judicial opinions are published by the government, such as the Supreme Court Reports. However, more cases are published by companies such as Westlaw and LexisNexis. For instance Westlaw publishes Federal Reports Annotated which contains many United States Circuit Court decisions. The cases are published by date. The advantage of using the reporters published by private companies is that they include, what is called key numbers that assist a legal researcher in finding additional material on specific topics addressed by a case.