Properties and Computational Algorithm for Fastest Quaternary Linearly Independent Transforms

Sixteen fastest quaternary linearly independent (FQLI) transforms are discussed in this paper. All the presented transforms can be derived using recursive equations and their inverse recursive definitions share common structure. In this paper, the fast flow graph equations and properties for the FQLI transforms are given. Based on the relationships between the spectra of the transforms, a recursive algorithm for the computation of their spectral coefficients is also proposed which reduces the total computational cost of generating their complete spectra. Experimental results for all the FQLI transforms as well as fixed polarity Reed-Muller transform over GF(4) are also given and compared in terms of the number of nonzero spectral coefficients. The comparison shows that for some quaternary functions the new FQLI transforms can give more compact representations.