Two classes of fixed polarity linearly independent arithmetic transforms for quaternary functions

Two classes of fixed polarity linearly independent arithmetic transforms (FPQLIA) for quaternary functions are introduced in this paper. These transforms are Kronecker-based and therefore can be calculated efficiently by fast transforms. Their basic definitions and fast flow graphs are shown. Relations between the different FPQLIA transforms are also presented and an algorithm for the optimization of FPQLIA is described which utilizes the given relation to reduce the computational cost. Experimental results for the transforms in terms of the number of nonzero spectral coefficients in the optimal FPQLIA transforms have also been given for several quaternary test functions and compared to the corresponding numbers for the optimal fixed polarity quaternary arithmetic (FPQA) transforms. The results show that for the set of quaternary test functions the numbers for FPQLIA transforms are on average 32% smaller than the ones for the FPQA transforms.