Abstract: A decoder is utilized for the correction of bit errors occurred in BCH (Bose-Chaudhuri-Hocquenghem) codes. The decoder first calculates the syndromes of a received word. The syndrome values form a first group of syndrome matrices whose determinant values are used for determining the weight of the error pattern of the received word. Subsequently, during each error trial testing, the bits constituting the received word are cyclically shifted and a predetermined bit is inverted to form a new word to see how the corresponding weight of the error pattern is changed thereby. If the weight is increased, the predetermined bit before being inverted is a correct one; otherwise if decreased the same is an erroneous one and thus correcting action is undertaken. The weight of the error pattern of a word is determined by the zeroness of the determinants of a plurality of matrices formed by the syndrome values thereof.

Abstract: A decoder is utilized at the receiving end of a digital communication system for correcting symbol errors occurred in a received digital information which has been encoded into a group of Reed-Solomon codewords. The method used in the decoder follows a modified step-by-step decoding procedure. The decoder first calculates the syndromes of a received word. The syndromes form a first group of matrices whose determinant values are used for determining the weight of the error pattern of the received word. Subsequently, each of the symbols constituting the received word is altered to see how the corresponding weight of the error pattern of the altered word is changed thereby. If the weight is increased, the symbol being altered is a correct one; otherwise if decreased the symbol being altered is an erroneous one and thus correcting action is undertaken.