A method of correcting a communication signal with BCH product codes is disclosed. The method comprising the steps of receiving a codeword vector, establishing a generator polynomial, establishing a check polynomial, calculating a binary-matrix, and calculating the binary syndrome S=Hr.sup.t. If an all zero vector results, no errors exist in the received vector. If errors exist, a tm x (N-k) binary matrix is created, the power basis expansion of (r(.alpha..sup.1), r(.alpha..sup.3), r(.alpha..sup.5), . . . r(.alpha..sup.2t-1)) is calculated, and the syndrome is solved. The speed of the method comes from using word-level XOR's to apply the check polynomial to the stream at all offsets. The utility of this approach is due in part to the fact that the conversion matrix involved can be created quickly using only items needed elsewhere in BCH decoders: a field table and the generator polynomial coefficients.Method of decoding signals having binary BCH codes769420706/04/201025/09/200620101,289Kline; Jason MichaelNewhart; Donald W.Nirschl; Nicholas PaulUS Patent and Trademark OfficeGoogle Patent Searchpatentimages.storage.googleapis.com/US7694207B1/US07694207-20100406-D00000.pngUniquemethodsupalphacheck polynomialbch product codesbinary bch codespower basis expansionerrorscodeword vectorbinary syndrome