Abstract: Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2^r)2ⁿ factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2^r)2ⁿ factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001). 

Key words: coding theory;consulting design;minimum aberration;mixed-level;regular, wordlength pattern