Brown filed the brief Friday, supporting a federal lawsuit challenging the constitutionality of California's ban on racial affirmative action in public university admissions, the Los Angeles Times reported.
In the brief, Brown said minorities face too high a barrier in efforts to overturn Proposition 209, which voters approved in 1996. Brown said because the proposition is part of the state Constitution and not just a law or university policy, it will be difficult to overturn it.
Brown noted a 2003 U.S. Supreme Court ruling that said race could be considered in college admissions as long as it didn't involve quotas or carry predetermined weight in decisions.
A federal appeals court last week struck down Michigan's ban on considering race and gender in college admissions.
A similar case seeking to overturn Proposition 209 is in the 9th U.S. Circuit Court of Appeals, which upheld the ban in 1997.