International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, pp. 8889

So far the multiplexing technique has been applied to pairs of vectors with similar types of parityrelated and/or conjugate symmetry properties, in particular the same value of .
It can be generalized so as to accommodate mixtures of vectors with different symmetry characteristics. For example if is Hermitiansymmetric and is Hermitianantisymmetric, so that is realvalued while has purely imaginary values, the multiplexing process should obviously form (instead of if both had the same type of symmetry), and demultiplexing consists in separating
The general multiplexing formula for pairs of vectors may therefore be writtenwhere ω is a phase factor (e.g. 1 or i) chosen in such a way that all nonexceptional components of and (or and ) be embedded in the complex plane along linearly independent directions, thus making multiplexing possible.
It is possible to develop a more general form of multiplexing/demultiplexing for more than two vectors, which can be used to deal with symmetry elements of order 3, 4 or 6. It is based on the theory of group characters (Ledermann, 1987).
References
Ledermann, W. (1987). Introduction to Group Characters, 2nd ed. Cambridge University Press.