  The most general class of non-locality criteria for N-partite d-chotomic
systems with k number of measurement settings is derived under the constraint
of measurement symmetries. It is the complete characterisation of the
multi-partite non-locality when the correlation is assumed to be symmetric
under the choice of measurement settings. The generalized non-locality
condition is obtained using the correlation functions, which are derived from
Fourier analysis of probability spectrums. It is found that the condition for
the local hidden variable (LHV) model is violated by multipartite quantum
states and general constraints for the quantum violation of maximally entangled
state has been obtained.
