Long, a data network specialist who deployed to Iraq from June 2008 to January 2009, is believed to be the only person who fired at officers, but authorities said they were unsure whether he had some kind of help.
"We are not ready to say he acted alone," state police spokesman Major Doug Cain said. Two "persons of interests" were detained in the nearby town of Addis.
Local media are reporting that one of the three fallen police officers served in both the Marine Corps and the Army: Matthew Gerald, 41.
WAFB Channel 9, a local CBS affiliate, reported that Gerald served as a Black Hawk crew chief while in the Army. He graduated from the Baton Rouge Police Academy in March, and leaves behind a wife and two daughters, according to the station.
The Marine Corps could not immediately confirm on Sunday that Gerald is a Marine veteran.
Long attended boot camp at Marine Corps Recruit Training Depot San Diego, and his last assignment was with the 3rd Marine Aircraft Wing at Marine Corps Air Station Miramar, California. During his time in the Marine Corps, Long also served with the 3rd Marine Division in Okinawa, according to his military records.
His military awards included: The Marine Corps Good Conduct Medal, Iraq Campaign Medal, Sea Service Ribbon, Global War on Terrorism Service Medal, National Defense Service Medal and Navy Unit Commendation Medal.
The Associated Press Contributed to this report.