Construction and decoding of BCH codes over finite commutative rings

AbstractBCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization ofx−- 1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings