A systolic power-sum circuit for GF(2m)

A systolic power-sum circuit designed to perform AB²+C computations in the finite field GF(2^m) is presented, where A, B, and C are arbitrary elements of GF(2^m). This new circuit is constructed by m² identical cells, each of which consists of three 2-input AND logical gates, one 2-input XOR gate, one 3-input XOR gate, and ten latches. The AB²+C computation is required in decoding many error-correcting codes. The paper shows that a decoder implemented using the new power-sum circuit will have less complex circuitry and shorter decoding delay than one implemented using conventional product-sum multipliers