Abstract: The invention comprises circuitry for systematically multiplying two arbitrary field elements in a Galois field GF(2.sup.m). Each element is represented by an m-bit binary number. The multiplicand field element is passed serially through a plurality of m-1 modulo multipliers. The multiplicand and the product from each of the m-1 modulo multipliers are passed through networks which are gated by bits of the multiplier field element forming partial products. The partial products are summed to form the bit representations of the final product.

Abstract: Apparatus for directly decoding and correcting double-bit random errors per word and for detecting triple-bit errors per word is disclosed. Said apparatus comprises a syndrome calculator which operates upon codewords received from memory and generates syndromes. The syndromes are operated upon and translated by a mapping device which generates pointers identifying the bits which are in error. The pointers are then passed through decoding means to generate error words which are summed with the received word from memory to provide a corrected codeword. The syndrome calculator may further provide a parity check signal to determine if a three-bit error is present, in which case the decoding means are not enabled and a signal is generated indicating that a triple-bit error has been detected which is not correctable.