TRANSFORM DECODING OF BCH CODES OVER ZM

For BCH codes with symbols from rings of residue class integers modulo m, denoted by Z(m), we introduce the analogue of Blahut's frequency d omain approach for codes over finite fields and show that the problem of decoding these codes is equivalent to the minimal shift register sy nthesis problem over Galois rings. A minimal shift register synthesis algorithm over Galois rings is obtained by straightforward extention o f the Reeds-Sloane algorithm which is for shift register synthesis ove r Z(m).