Multidimensional polynomial algebra for bubble circuits

The paper expands the basic concepts of the coding theorists in the representation of data strings by algebraic polynomials, and develops the representation of both time and location of individual binary positions in the same polynomial. Further, it advances a set of algebraic operations on such polynomials to correspond to the various subfunctions that are accomplished in the actual domain circuits. The specific applications of the techniques proposed in this paper for the design and synthesis of such circuits is presented in a companion paper.