  One of the problems concerning entanglement witnesses (EWs) is the
construction of them by a given set of operators. Here several multi-qubit EWs
called stabilizer EWs are constructed by using the stabilizer operators of some
given multi-qubit states such as GHZ, cluster and exceptional states. The
general approach to manipulate the multi-qubit stabilizer EWs by
exact(approximate) linear programming (LP) method is described and it is shown
that the Clifford group play a crucial role in finding the hyper-planes
encircling the feasible region. The optimality, decomposability and
non-decomposability of constructed stabilizer EWs are discussed.
