Fastest classes of linearly independent transforms over GF(3) and their properties

New fastest linearly independent (LI) transforms over Galois field (3) (GF(3)) and their corresponding polynomial expansions have been introduced. The number of required additions and multiplications in new LI transforms is lower when compared with the ternary Reed-Muller transform, which was previously known as the most efficient transform over GF(3). The paper discusses various properties of these fastest LI transforms and their corresponding polynomial expansions over GF(3) as well as their comparison with the ternary Reed-Muller transform. Experimental results in one class of fastest LI transforms for some ternary benchmark functions are also shown here and compared with those of the fixed polarity Reed-Muller transform over GF(3).