It is very powerful for constructing nearly saturated factorial designs to character-iza fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary worldength pattern of a regular symmetrical fractional factorial split-plot (FFSTP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial dwsign theory and coding theory, we obtain some general and unified combinato-rial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to theses identites, we further estab-lish some general and unified ruleds for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.