Computations in Galois field using multiple-valued logic

A unique encoding technique to perform arithmetic operations in Galois field using multiple-valued (MVL) is presented. The computations are done in a quaternary logic system that can replace the binary one. To show that both systems are equivalent, we illustrate computation examples of inversion and exponentiation in Galois field using AB² technique (where both A and B are elements in Galois field). Multi-level representation of signals lies between a hard decision binary system and fuzzy system whose value ranges from 0 to 1.