Local　coordinate　coding　(LCC)　is　a　framework　to　approximate　a　Lipschitz　smooth　function　by　combining　linear　functions　into　a　nonlinear　one.　For　locally　linear　classification,　LCC　requires　a　coding　scheme　that　heavily　determines　the　nonlinear　approximation　ability,　posing　two　main　challenges:　1)　the　locality　making　faraway　anchors　have　smaller　influences　on　current　data　and　2)　the　flexibility　balancing　well　between　the　reconstruction　of　current　data　and　the　locality.　In　this　paper,　we　address　the　problem　from　the　theoretical　analysis　of　the　simplest　local　coding　schemes,　i.e.,　local　Gaussian　coding　and　local　student　coding,　and　propose　local　Laplacian　coding　(LPC)　to　achieve　the　locality　and　the　flexibility.　We　apply　LPC　into　locally　linear　classifiers　to　solve　diverse　classification　tasks.　The　comparable　or　exceeded　performances　of　state-of-the-art　methods　demonstrate　the　effectiveness　of　the　proposed　method.