Complete Bionic Commando Rearmed with the following tasks completed to get codes to unlock the 'Purple Matrix', 'Retro Oufit', and 'Prototype Weapon' in Bionic Commando (codes vary between PlayStation3 consoles).
Unlock Retro Outfit: The code is already unlocked in the Database in Bionic Commando: Rearmed.
Unlock Prototype Weapon: In Bionic Commando: Rearmed, find the floating FSA icon in Area A. It is located behind an electrical barrier you must backtrack to after removing. This will unlock the code in the Database.
Unlock Purple Matrix: In Bionic Commando: Rearmed, go to Area 0 and look for the open Yashichi door after collecting ALL 12 Yashichis. Collect the 'Purple Matrix' inside. This will unlock the code in the Database.