A SYSTOLIC POWER-SUM CIRCUIT FOR GF(2(M))

A systolic power-sum circuit designed to perform AB(+) + C computation s in the finite field GF(2(m)) is presented, where A, B, and C are arb itrary elements of GF(2(m)). This new circuit is constructed by m(2) i dentical cells, each of which consists of three 2-input AND logical ga tes, one 2-input XOR gate, one 3-input XOR gate, and ten latches. The AB(2) + C computation is required in decoding many error-correcting co des. This brief contribution shows that a decoder implemented using th e new power-sum circuit will have less complex circuitry and shorter d ecoding delay than one implenmented using conventional product-sum mul tipliers.