On the fundamental structure of Galois switching functions

In connection with investigations conducted by Menger (1969), Benjauthrit and Reed (1976), and Pradhan (1978) two methods have been reported for deriving a unique Galois switching function from a given truth table description of the function. However, neither of the two methods appears satisfactory. One method often contains many redundant terms in its formulation, whereas the second method requires a great number of multiplications and additions. By some algebraic manipulations, an expanded formula is obtained which combines the best features of both methods. This formula makes it possible to compute the coefficients of the desired function more directly and probably with less effort. The conduction of calculations by means of the new formula is illustrated with the aid of examples.