AN ALGEBRAIC COMPLETE DECODING OF DOUBLEERROR-CORRECTING BINARY BCH CODES

An algebraic complete decoding of double-error-correcting binary BCH codes is shown in this paper. It is faster than Hartmann s decoding of double-errcr-correcting binary BCH eodes of primitive length. And when the weight of the error pattern corresponding with synlromes S1 and S3 is equal to 3, this deeoding can find all error patterns of weigth 3 with the same syndromes. On the other hand, a discrimination of judging whether or not a cubie equation over GF(2m) has three distinct roots in GF(2m) is also shown in this paper. It is very improtant in the complete decoding of triple-error-correcting binary BCH codes.