Based on basic theory of cyclotomic coset, the concepts of decomposition of defining sets for binary and quaternary BCH codes are introduced respectively this decomposition of defining sets builds up a bridge among the Euclidean orthogonal decomposition of binary BCH codes and Hermitian orthogonal decomposition of quaternary BCH codes. Then the orthogonal decomposition of the dual codes of binary and quaternary BCH codes is also presented. Furtherly, the decomposition of the defining sets of primitive binary and quaternary BCH codes with given designed distances is well studied and solved. Applying the results, some entanglement-assisted quantum codes with good parameters are constructed. The method proposed in this paper devised a new scheme in determining the optimal number of entangled bits, which can simplify the theoretical derivation in constructing entanglement-assisted quantum error correcting codes from classical BCH codes, and also be useful for studying general constructions of entanglement-assisted quantum error correcting codes from cyclic codes.