CLASSIFICATION OF NEW LINEARLY INDEPENDENT TRANSFORMS OVER GF(3)

Abstract

New classes of ternary linearly independent transforms as the bases of ternary polynomial expansions over GF(3) are introduced here. Recursive equations defining the linearly independent transforms and their corresponding butterfly diagrams are shown. Various properties and relations between the introduced classes of new transforms are discussed. Computational costs to calculate linearly independent transforms over GF(3) and applications of the corresponding polynomial expansions in ternary logic design are also presented.