A　SO(3)　transformer　of　a　three-plate　polarizer　is　adopted　to　rapidly　achieve　the　transformation　of　the　polarized　state.　The　polarization　coding　based　on　Stokes　components　S2　and　S3　is　analyzed　and　demonstrated.　Tabu　search　algorithm　is　used　to　accelerate　the　transformation　of　the　polarized　state　by　utilizing　Mueller　matrix　roots　decomposition　to　decompose　the　SO(3)　matrix,　and　substituting　first　order　Taylor　series　approximations　for　the　trigonometric　functions　in　the　SO(3)　matrix.　The　results　show　that　bias　voltage　is　less　than　120　V　in　the　coding　zone.　The　search　speed　of　our　algorithm　is　faster　than　the　one　without　first　order　Taylor　series　approximations　by　4　times.　©　2015,　Technical　University　of　Wroclaw.　All　rights　reserved.