Narrow Results

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.

Two new fixed polarity linear Kronecker transforms executed over GF(3) are introduced in this article. Both transforms are based on recursive equations using Kronecker products what allows to obtain simple corresponding fast transforms and very regular butterfly diagrams. The computational costs to calculate the new pair of transforms and their experimental comparison with ternary Reed–Muller transform have also been discussed for the purpose of using their error correcting properties that are useful in circuit testing and verification.

A new algorithm that efficiently calculates fixed polarity Reed–Muller (FPRM) expansions for ternary functions is presented in this paper. The algorithm starts from the truth vector representation of a ternary function and recursively generates all elements of the input function's polarity matrix. Computational costs for this algorithm are derived and they are smaller than in other existing methods for generating the complete polarity matrix when n ≤ 3.

This paper introduces two new classes of recursive fast transforms over GF (3). They are based on recursive equations using Kronecker products that allows to obtain simple corresponding fast transforms and regular butterfly diagrams. The computational costs to calculate both classes of new transforms and the experimental results comparing introduced transforms with ternary Reed–Muller transform are also presented.