Transform decoding of BCH codes over Z_m

Abstract

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 domain approach for codes over finite fields and show that the problem of decoding these codes is equivalent to the minimal shift register synthesis problem over Galois rings. A minimal shift register synthesis algorithm over Galois rings is obtained by straightforward extention of the Reeds-Sloane algorithm which is for shift register synthesis over Z_m.