Family of Fastest Linearly Independent Transforms over GF(3): Generation, Relations, and Hardware Implementation
B. J. Falkowski, C. C. Lozano and T. Luba
New linearly independent (LI) transforms that operate over Galois Field (3) (GF(3)) and their corresponding polynomial expansions are presented in this article. All the presented transforms can be calculated efficiently by fast transforms and the calculation requires fewer number of additions and multiplications compared to the well-known Reed-Muller transform over GF(3). Based on the structure of their butterfly diagrams, the transforms are categorized into four types. Formulae for fast transform calculation of each type are given. Relations that exist between the transforms are also presented, which allow some of the LI transforms to be calculated from one another with reduced computational cost. Finally, the hardware calculation of their spectra are shown based on systolic array processor.