Reduced circuit implementation of encoder and syndrome generator
An error correction method and system includes an Encoder and Syndrome-generator that operate in parallel to reduce the amount of circuitry used to compute check symbols and syndromes for error correcting codes. The system and method computes the contributions to the syndromes and check symbols 1 bit at a time instead of 1 symbol at a time. As a result, the even syndromes can be computed as powers of the odd syndromes. Further, the system assigns symbol addresses so that there are, for an example GF(2.sup.8) which has 72 symbols, three (3) blocks of addresses which differ by a cube root of unity to allow the data symbols to be combined for reducing size and complexity of odd syndrome circuits. Further, the implementation circuit for generating check symbols is derived from syndrome circuit using the inverse of the part of the syndrome matrix for check locations.