Generalised hybrid arithmetic canonical expansions for completely specified quaternary functions

A novel representation of completely specified quaternary functions, called `hybrid arithmetic canonical expansion´ is shown. The new expansion is based on both standard and GF(4) algebra. The transform matrix of the expansion is defined by an arbitrary set of linearly independent functions in GF(4). The introduced expansion is generalised by applying to it the concept of polarity. The way of obtaining the coefficient vector of the expansion from some coefficient vector in known polarity is introduced. Generalised hybrid arithmetic polynomial expansions for known basis functions from quaternary Reed-Muller transforms are shown. The idea of binary and ternary independent function is extended to the quaternary case and the new expansion for such a matrix is also presented. The hybrid arithmetic expansion is for completely specified quaternary. Finally, implementation of the generalised hybrid arithmetic expansion in the form of a suitable universal logic module is introduced