  We study genuine tripartite entanglement and multipartite entanglement in
arbitrary $n$-partite quantum systems based on complete orthogonal basis (COB).
While the usual Bloch representation of a density matrix uses three types of
generators, the density matrix with COB operators has one uniformed type of
generators which may simplify related computations. We take the advantage of
this simplicity to derive useful and operational criteria to detect genuine
tripartite entanglement and multipartite entanglement. We first convert the
general states to simpler forms by using the relationship between general
symmetric informationally complete measurements and COB. Then we derive an
operational criteria to detect genuine tripartite entanglement. We study
multipartite entanglement in arbitrary dimensional multipartite systems. By
providing detailed examples, we demonstrate that our criteria can detect more
genuine entangled and multipartite entangled states than the previously
existing criteria.
