Cyclic code check bits generation and error correction using sum of

Abstract

Check bits for a cyclic code are generated for a binary integer by first obtaining a remainder value for each bit of the integer resulting from dividing the bits of the integer by a cyclic generator polynomial to obtain a quotient and said remainder. All remainders are then summed modulo 2 to obtain an integer remainder which functions as the cyclic code for the binary integer. An error in a received integer can be identified and corrected by generating new cyclic code check bits for the received integer, and then comparing the new cyclic code check bits to the received cyclic code check bits. Any difference between the two check bits will correspond to the unique remainder for an erroneous bit, which can then be corrected by complementing the bit. If two or more errors are present, an error will be recognized but the specific errors cannot be identified. The integer must then be discarded. In a preferred embodiment the remainder values are added in an exclusive OR circuit in which remainder values for adjacent bits are summed, and adjacent sums are summed to obtain a final remainder value for all bits.